Before I get into the tutorial, let me begin with a description of what exactly it is that you are trying to do. You want to pick up stitches in a straight line perpendicular to the rows that you were knitting on the body of the sweater. This means that you will want to pick a column of stitches and pick up and knit from the same part of the stitch in every stitch in that row.
I like picking up one of the bumps in between the stitches. Take a look at your knitting and see how garter stitch has "top" bumps and "bottom" bumps. It does not matter which you chose so long as you stay consistent.
Here is one way to find the "in between" bumps. Run a needle through the top bump of a column of stitches:
See how the needle runs through the same part of each stitch in the column? Now comes the tricky part since we are working at the edge of the knitted fabric, where garter stitch can get a little odd looking. (Of course, you could always work a stitch or so in from the edge to make this easier but I try to avoid that since the seams get quite bulky) Find the bump immediately next to the first bump (the one with the needle in it) towards the edge of the garment. If your first bump was a "top" bump the then one next to it will be a "bottom" bump and vice versa. Run a second needle through this column of bumps.
You will see how that loop can look different depending on the tension of the row but if you start by finding a recognizable column of bumps, you can always find the edge loop/bump by moving one bump towards the edge from your starting point.
One other tip before we get started: count out how many stitches you will need to pick up (for garter it is one stitch per one row; stockinette will vary according to the relationship between your stitch and row gauges but that is for another time) and mark the end points. I like paper clips. They are cheap, colorful, and you never feel bad when you inevitably lose one.
Now onto the actual tutorial.
Option #1: Sliding in a knitting needle and knitting right off it.
That is about all there is to it. Find the column of stitches in which you want to pick up and knit for the sleeve and then slide a knitting needle into the stitches of the column. Make sure that you have the same number of stitches on either side of the shoulder (if you need to pick up 44 stitches, you would have 22 on the front and 22 on the back).
See how all of the pick-up loops are in the same column. This makes for a neat and clean edge of the sleeve and shoulder.
Here you can see stitches for an entire sleeve ready to go. We have not knit anything yet, just picked up stitches in preparation for it. You can also see the paperclips marking the sides of the sleeve.
Now just go ahead and knit across that row of stitches.
That was not too bad now, was it? Ready for option number 2?
Option #2: using a crochet hook to pick up and knit
This method is very much like the first: pick a column of stitches to follow and stick with it. Now, instead of running a knitting needle through the bumps and then knitting across them, you will insert a crochet hook into the bump and draw the working yarn back out.
Take a crochet hook the same size as your knitting needle or a bit smaller and insert it through the bump as if to knit. Go ahead and tug with your left hand (the one holding the knitted piece) if you need to in order to get the crochet hook in there.
Have your working yarn ready to attach - as if you were just starting another ball - with a tail off to the side to weave in later (you can knit it in on your next knit row). With the yarn and crochet hook in your right hand, catch the yarn in the hook and draw it through the bump and onto the body of the crochet hook.
Once you have a number of these loops, go ahead and transfer them off the crochet hook and onto a knitting needle.
Repeat until you have picked up all of the sleeve stitches.
The end result of option 2 is a bit different from that of option 1: now you have "knit" across the row and your working yarn is waiting for you to work a wrong-side row back across the sleeve to start the pattern.
Option #3: Picking up and knitting all in one motion
I like this the best because it is the most efficient use of time. However, there is often quite a bit more manhandling of the fabric involved and can be somewhat tricky if you are not quite sure in which bump you are picking up.
Like with option 2, stick your knitting needle into the appropriate bump as if to knit.
Now, with your working yarn at the ready, wrap the yarn around the needle just like you were knitting (which, in fact, you are). Here comes the tough part. You need to get that loop around the needle out from under the bump and squarely onto the right hand needle as a full-fledged knit stitch. The trick: firmly grasp the knitted fabric with your left hand and give it a tug down and to your left (not too hard) just enough to open up that bump/loop and let you slip the right hand needle out. This is just like knitting except that your left hand has to do the work of the left needle in giving you a clear loop through which to work.
See the tug:
At the end you have a knit stitch without having to move it from one needle (or crochet hook to the other).
None of these options is any better or worse than any other. One might work better for a particular type of yarn, etc. Just pick whichever one feels most comfortable. And remember - if something doesn't work, just frog it. After all, it is not as if you have to worry about undoing an entire sweater accidentally, at worst it is just a few stitches.
What is that green garter stitch at the top of the post? My Baby Surprise Jacket. It turns out that I have the attention span of a gnat and could only remember to work shaping on one end of the row for the last few garter ridges and I am going to have to frog a bit. I just do not have the heart to do it tonight.
