One of the aspects about increasing that many people find tricky is doing it in a pattern, and incorporating the new stitches into the pattern stitch. We'll talk about how it works generally, and then look at the specific cases of ribbing and seed stitch since those come up frequently.
It's going to simplify the following discussion if we first look at how successive increases affect the structure of the fabric. Typically, patterns will call for successive decreases to be done at the same place in relation to an edge of the fabric -- that is, you'll be asked to work 1 or 2 stitches, do an increase, and then work to the same distance from the other edge and do an increase, on each of several increase rows. This means that your second increase is going to be between this fixed edge stitch and your first increase, and so on. This is going to affect your choice of stitch for each of the increased stitches as you incorporate it into the pattern.
A second concept that's helpful to understand is that you will be temporarily out of pattern as you work your initial increases. A well-crafted pattern will have a number of increase rows that's a multiple of the number of stitches in your stitch pattern; for instance, a pattern where you're increasing in seed stitch, a 2-stitch pattern, should have an even number of increase rows, while a pattern in K2P2 ribbing should have a multiple of 4 increase rows. This will enable you to work your way back into the pattern, but being off during the interim is inevitable.
So, let's look at how this works, using seed stitch as an example. Let's say that we're working on a seed-stitch sleeve, and our pattern tells us, "Increase 1 st on each end every 8th row, 6 times." Let's further say that the pattern is well-written, and therefore we have a stockinette selvedge of 1 stitch (to make seaming clean and easy), and an even number of stitches in seed stitch (so that after doing our easy seam, the pattern will flow smoothly across the seam, rendering it invisible); therefore, the RS row directions are "k1, (k1, p1) to last st, k1," and the WS directions are "p1, (p1, k1) to last st, p1." Now, as we've already discussed, a KFB type of increase is the best choice for seed stitch, and it can be placed on the second stitch in from each edge; as to the specific type, we'll choose between KFB and PFB based on the type of the stitch that the increase will be done on, and do a mirrored version for the increase at the left edge so that the new stitch appears before the stitch where the increase is done and not between that stitch and the edge stitch.
Let's briefly review the mirrored front-and-back increases. These are done like so: slip a stitch knitwise and put it back on the left needle with its left leg in front; work (in either knit or purl, as appropriate for the original stitch in pattern) into the left leg and let the old stitch go; pick up the old stitch again using the tip of the left needle; work (in either knit or purl, the same as used for the first stitch) into the right leg of the stitch. This gives you your twisted stitch with the bar around it first, and your untwisted stitch with no bar second, which is the exact reverse of the standard front-and-back increase.
Looking at the first increase row, we'll knit the selvedge stitch, then do the increase on the following stitch, which is a knit, so that will be a KFB. We'll then work in seed stitch as established, doing (p1, k1) across until we reach the 2nd stitch from the end; this one is a purl, and we want to have the new stitch appear first, so we'll do mirrored-PFB here, and then knit the final selvedge stitch.
Now, let's look at the first WS row after this increase, which is where you have to make the decision for the first time on how to work that new stitch into the pattern. We'll purl the selvedge stitch, then purl the first stitch of the seed-stitch pattern, and the next one is the new stitch. Subsequent increases are going to come in between these two stitches, separating this new stitch from its "parent" (I'm going to use that as the term for the stitch that the increase was done into), but it's always hereafter going to be adjacent to the stitch that follows it. Therefore, you want to work the stitch as the type of stitch that should be adjacent to that following stitch, rather than the type that the pattern says should be adjacent to the parent stitch. The following stitch is going to be knit on this row, and therefore the new stitch should be purled; this does, temporarily, give you two purls in a row, but that's okay. You'll then (k1, p1) until you have 3 stitches left in the row, which are the other new stitch, its parent, and the other selvedge; by the same reasoning as above, you will knit the new stitch and also knit its parent, and then purl the selvedge stitch as always. The other WS rows between this row and the next increase row will be worked in exactly this same manner; RS rows will be "k1, k2, (p1, k1) to last 3, p2, k1" (yes, I could have said "k3" at the start -- but I think this makes it clearer). You are slightly out of pattern for the 7 rows between the two increase rows. However, since what you have is a 2-column strip of garter stitch on the edge of your seed stitch, it's not at all obtrusive; you can take my word for that, or you can swatch it up and see what it actually looks like.
Now, let's see what happens on the second increase row. Again, you're going to place the increases on the second and second-to-last stitches of the row, and since those stitches haven't changed, these are going to be a KFB and a mirrored-PFB respectively. Therefore, this row will be "k1, KFB, (k1, p1) to last 2 stitches, m-PFB, k1." On the following WS row, you'll purl the selvedge stitch and purl the parent; the stitch that follows the new stitch is the same one that was new during the first increase, and was purled on the WS rows, and therefore the new stitch for this row should be knitted on the WS to be compatible with that, and just like that, you're back in pattern. Continue on across the row, and end by purling the new stitch between the two knits over there. You're now completely back in pattern until the next increase row comes along. You'll continue in this fashion, getting out of pattern on the odd increase rows, and back into it on the evens, until you've done all the increases.
Increases in ribbing are similar. Let's look at a 4-stitch pattern instead of a 2-stitch one, and just to make it a bit different, let's suppose we're doing a ribbed sleeve in the round. Let's say that our rounds are set up so that the beginning of the round is in the middle of a knit rib, so that our ribbing directions are "k1, p2, (k2, p2) until 1 st remains, k1," and that our increase directions are "Inc 1 st at beginning and end of round, every 6th round, 8 times." Since we're working in the round, there's no need to maintain a selvedge for seaming; an increase can be done in the very first or very last stitch of the round, and therefore we can do a KFB in the first stitch, and a mirrored-KFB in the last stitch, on each increase round. As with the seed-stitch example above, each successive increase will appear between the "parent" stitch and the prior increase, so the new stitches should be worked in pattern with the stitch outside the increase. Therefore, on the first and second increase rounds, the new stitches will both be knits, and you'll have a band of first 4 and then 6 knits up the inside of the sleeve. On the third increase round, however, the new stitches will be purls, so you'll have a single purl rib separating your new 2-knit ribs from the original center rib, and then after the 4th increase round, you'll have a 2-purl rib on either side of the original center knit rib, and you'll be back in pattern; the 5th through 8th increase rounds will just be a repetition of the first four.
So far, we've only looked at cases where the parent stitch is always a member of the same column, so the second and subsequent increases are spawned between the parent and the prior increase. This is by far the most common placement. You can, however, have cases where the parent column changes from one increase row to the next, with subsequent increases being done from the column which was new in the prior increase, and this has two effects which are different from what we've looked at so far: first, each increased stitch will stay adjacent to its parent, rather than being pushed away by the following increase, so it will need to be "in pattern" with respect to its parent, rather than with respect to the stitch beyond; second, because the parent column is different every time, the type of increase used will vary, rather than staying constant as it's done in our prior examples. This is a somewhat related concept to the concept of strong and feathered decreases, which either have a single surviving column or a change of surviving column each time.
A place where these "feathered increases" might be used to good effect would be in the thumb gusset of ribbed mittens or armwarmers, so let's look at some very simple knitted armwarmers as an example -- these will be just a tube with a thumb, and since they're totally lacking in fingers, the thumb can be placed right at the side, with no adjustment for left and right hands. Let's suppose a fingering-weight yarn, and a cast on of 48 stitches in k2p2 rib. After working to the desired length for the wrist, our first increase row will be "mKFB, KFB, place marker, p2, (k2, p2) to end"; subsequent increases will be "increase in 1st st of round and last st before marker, every 3rd round, until there are 18 sts before marker."
Here's how this works out. On the first increase round, you're doing a mirrored KFB into the first stitch of the round, which is a knit stitch, and a regular KFB into the second stitch, which is also a knit stitch, and then you're placing a marker, and finishing the round. On the following 2 work-even rounds, the stitches that were increased will be purled, since a purl stitch is what should be adjacent to each of the parent stitches. On the second increase round, you're going to be doing the increases into the columns that were new last time, and since those are both purls, the new increases will be a mPFB and a PFB. Those stitches will also be worked as purls on the work-even rounds, since you want a 2-purl rib on either side of the 2-knit rib you started with, and the increase on the 3rd increase round will also be mPFB and PFB. For the work-even rounds that follow this increase, you'll be knitting the new columns, and then the increases in the 4th increase round will be mKFB and KFB.
By now you should be seeing how this works; you'll have a total of 8 increase rounds, increasing 2 purls, 2 knits, 2 purls, and 2 knits, on either side of the original 2-knit rib you started with. This produces a very interesting gusset, with the new ribs starting sort of from nowhere rather than seeming to spawn off of another column as they would if you did strong increases.
If you'd like to actually knit up some armwarmers like this, I've written up a pattern for them, and you can find that right over here. If you're on Ravelry and want to add it to your queue, here's the link for that.
That should give you a pretty good grasp on the basics of incorporating increased stitches into a pattern. I do have a bit more to say on the topic -- in particular, I want to talk about how one works increases into a lace pattern -- but I think I want to do it in a slightly more generalized way, looking at the decreases also, so I'm going to do that separately. Stay tuned!