At its most basic, knitting work comes down to two moves: the knit and the purl. The ways you combine those two moves create the basic knitting stitches. It all comes down to deciding where you want the yarn bump to go. Do you want the yarn bump (commonly called the purl bump) to go in back? That calls for a knit stitch. If you want the yarn bump to be on the side facing you, you purl. There are several standard combinations that make up the basic knitting stitches.
The most basic knitting stitch is garter stitch, which is knitting every stitch (or purling every stitch). The right and wrong side of your work will look identical as every other row has those bumps, so a garter stitch project is reversible. Not many patterns call for an entire project to be done in garter stitch. Instead, garter stitch is more often used as a border. I personally like garter stitch for comfort items, like blankets and shawls. It is a more rustic look than the more common and polished-looking stockinette stitch. And because it's all knit with no need to think about switching stitches, even between rows, projects go quickly. A giant triangle shawl I made for my sister took no time at all because it was all garter stitch.
The most common knitting stitch for most projects, especially sweaters, is stockinette stitch. Stockinette stitch is created by knitting on the right side of the work and purling on the wrong side. This results in that beautiful "v" effect. Stockinette stitch (sometimes also called stocking stitch) is more than any other basic knitting stitch the reason for there being a right side of your project and a wrong side. The right side is the "v" side and the wrong side is the side with all the yarn bumps.
If an entire piece is knitted in stockinette stitch, the piece will roll up. This can be a great effect if you're knitting a rolled brim hat. I have a cardigan sweater that called for the rolled edges because it lends a casual flare to the look. But generally if you're trying to knit something flat, like a sweater, blanket, or scarf, you need to add an edge in some other stitch to prevent the roll-up. That edge can be done in a couple of ways. For the cuffs and bottom edges of sweaters, you'll often edge with a rib stitch. The other common edge is worked in garter stitch, worked for something like 4 rows at the bottom or 4 stitches on each side.
When you start combining knits and purls on the same row, you can make even more basic stitch styles. The rib is worked by alternating knits and purls to create a vertical striped effect. The most common ribs are 1x1 and 2x2. A 1x1 rib is just knit 1, purl 1. Then on the wrong side, you knit the purls and purl the knits. This will create the stockinette "v" effect one column of stitches at a time. A rib stitch makes a great cuff or bottom edge to a sweater because of its ability to stretch and then contract again.
Seed stitch is the opposite of the rib. It's a knit 1, purl 1 combination. But on the wrong side, instead of working in a stockinette principle of keeping the yarn bumps on the same side for each column of stitches, you work in a garter stitch principle. So you knit the knits and purl the purls. Some think the purl bumps scattered across the fabric look like seeds, hence the name. Like garter stitch, seed stitch will produce a reversible fabric. The texture of seed stitch makes it a great choice for wash cloths.
You can vary the seed stitch in a couple of ways. The moss stitch is a knit 1, purl 1 stitch, like the seed stitch. But you don't switch the knits and purls every row. Instead, you would work two rows where you kept the yarn bumps on the same side of the project. Then the next two rows would switch the yarn bumps to the other side. A moss stitch pattern worked in an even number would be:
A double seed stitch is also a four-row pattern, like the moss stitch, but just involves two stitches instead of one. So knit 2, purl 2. (The above picture is of a double seed stitch.)
So far, so good, but there's a twist. All of the above stitches are the opposite if you're working in the round. To make stockinette stitch in the round, you knit every stitch. Alternating between knit rows and purl rows in the round makes garter stitch. When you look at your knitting in the round, you'll understand why this is. Because you're never turning and going back the other direction, you are always facing the same side of the project. Thus, knitting always puts the yarn bump on the back side and purling always puts the bump on the front side.
Likewise, rib and seed stitch are a little different when worked in the round as well. Just as in stockinette in the round, you'll need to remember that to create a rib in the round, you will keep the yarn bumps in each vertical column of stitches on the same side of the fabric by knitting the knits and purling the purls. By the same token, to create the alternating look of seed stitch, you now must do the opposite and knit the purls while purling the knits.
Once you have these basic knitting stitches down, there is no end to the ways you can combine them. You can create an interesting texture to a blanket by mixing squares of garter stitch, stockinette, seed stitch, or moss stitch. And then there are broken rib and traveling rib patterns. The possibilities are endless!