Most tutorials use contrasting yarn to aid in the visual representation. I always find that somewhat annoying because then I don't know what to expect when I use the same yarn as the garment was knit in, so I'm going to show you with the same yarn and hope that I don't confuse you horribly. You can click on the photos for larger images.
Step One: Block your pieces.
This is critical. The edges lie down, the stitches open up, and all your edges are blocked to matching lengths. Those schematics in your patterns are really important.
Step Two: Sew the shoulder seams.
There is a prescribed order for sewing your sweater together. It's all about the sleeves. Begin by laying your front and back pieces flat, right side up, with the shoulders lined up. If you are a wise knitter (and I'll admit that I seldom am), you will have left a long enough tail when binding off that you can use it to seam your shoulders together. A length of the shoulder seam plus one half of that length ought to do the trick.
Run the yarn through each corner on the arm-hole edge of the pieces (you'll see I had to use a different piece of yarn because my tail wasn't long enough). You will work on each piece in this same order (I did front, then back here, but back, then front works just as easily).
The next step is true of garter and stockinette pieces: find the "v" of the nearest knit stitch in the piece you threaded first (here the front) and run your needle behind that "v". Pull the yarn through.
Do the same for the other piece. Here the back is upside-down, but the "v" I have picked up is in the same direction as the one I picked up on the front. This is will put you a half-stitch off, but it will look nicer and won't make the slightest difference in the long-run. If you are doing a stockinette stitch garment, choose "v"s that are one stitch away from the bound-off edge or you'll get an annoying bump right where you are seaming. Garter stitch does this automatically because the knit stitches are each a purl bump away from the bind-off row, if that makes sense.
Continue picking up every "v" on each side until you get to the end.
Weave in the ends. Since you get this lovely seam on the inside, I like to weave my ends back and forth through it like this for several stitches.
There you have a lovely shoulder seam!
Step Three: Set in sleeves.
Sleeves are hard enough to explain as it is and this sweater's sleeves are oddly shaped, so I won't go into detail yet, but I will tell you that as soon as the shoulders are seamed, clip or pin the sleeve into the armhole and seam it flat this way, taking each clip out as you get to it. This assures that the sleeve remains perfectly fitted to the armhole. I'll try to show you some tricks when I get to seaming my Exeter's sleeves, but it's largely an improvisational seaming experience.
Step Four: Sew the sides and sleeve seams.
These are my favorite seams! You need a length of yarn 3-4 inches longer than the seam you want (or longer if you wish to be more cautious). You can seam all the way from the bottom edge of the sweater out to the cuff of your sleeve if you want or have each seam meet under the arm. It's up to you and it works either way.
Match the sides (you'll see I was naughty and forgot to do my shoulder seams and sleeves first, oops! Trust me, it only makes things harder for you!). You can clip them like the sleeves if you want.
Run the yarn through the lower corner of each piece. You will alternate between the pieces in the same order that you run the needle through, just as for the shoulder seams.
When doing an invisible seam in garter, catch the garter bumps, not the knit stitches. I don't think it matters terribly which ones you catch as long as you are consistent and you skip the edge stitch. Edge stitches are ugly and should always be ignored. A purl ridge consists of bumps that go over and bumps that go under. I have gone through one that goes over because the yarn I am drawing through will look like a bump that goes under (a later photo will illustrate this better).
(I can't get these next two photos to upload turned the right direction, so sorry about that. I'll try to fix it!)
Continue in this manner for an inch or so. Here you can see the zig zag of my yarn and (hopefully) how it goes into each purl bump better than I explained it earlier.
Tug the ends of your seaming yarn (not too tightly, though!). Ta-da! It's invisible! Cool, eh? I always get a seam-y indent, so it's never really invisible, but I've had some pretty darn close ones before. The second photo is what the wrong side looks like. Very tidy.
Now to invisible seam stockinette: insert your needle into the middle of the second "v" from the edge (remember those edge stitches are silly and to be ignored). With a little wiggle or some fishing you should be able to find and catch a bar in there. Here it is fished out:
Do the same on the other piece. I was seaming a fingering weight sweater, so instead of catching the bar of every stitch, I skipped one. I find this gives a little better drape with just as much support and it's both less tedious and easier to fudge (because you don't always have an equal number of rows on each piece and some times you have to skip an extra one here and there to get it to match up perfectly). Here's how it shapes up: (again, sorry about the orientation)
I hope this is at least somewhat enlightening. As long as it isn't entirely confusing, I'll be happy. I'm also happy to answer any questions! Either here or on Ravelry. Wednesday I have lots of exciting progress and projects, so I'll see you then (with a more timely post)!