OK, here's another practice exercise:

Cast on 26 stitches

Row 1: (K2, p2) across to last two stitches, k2. This is a four-stitch repeat, because the bit inside the parentheses (which serve to indicate the pattern repeat) is 4 stitches wide - two knits, and two purls. So you'll just do that over and over - k2, p2, k2, p2, and so on, until you have two stitches left on your left needle. Knit those two stitches.

Row 2: (p2, k2) across to last two stitches, p2. This row is the opposite of Row 1. See what's happening? You're building narrow columns of stockinette stitches, two stitches wide. So your knits will always be stacked on your knits, and your purls will always be stacked on your purls. The fabric at this point is also, actually, reversible. Both sides look equally good, because the backside of the purls on Row 1 is a pretty column of knits, and the backside of the purls on row 2 does the same thing!

Repeat Row 1 and Row 2 for several more rows, or until you think you have the hang of it. You'll always be able to tell if you're on a Row 1 or a Row 2 based on what the first stitch should be - if you start the row looking at a purl, you're on a Row 2 (since it begins with p2). If you start the row looking at a knit, you're on a Row 1. Also - as an aside - this is called "reading" your knitting. And if you're a really proficient knitter, then you'll be able to read your lace or cables, find a mistake six rows down, ladder down to fix it, pick up the stitches in order, and no one will be any wiser. Or if you're me, you'll read your lace, find the mistake, throw the damned shawl across the room and cast on for a pair of socks instead.

A ribbing at its most basic level can be made from any alternating number of knits and purls - the cuff of your sweater, for example, is something like k1, p6 (viewed from the outside - "right" side), or p1, k6 (viewed from the inside - "wrong" - side). Most ribbings are described in shorthand as "__ by __" or "__ x __". For example, I often use 3x1 on sock cuffs. Any knitter will know what that means - k3, p1. And later there's twisted rib, and mistake rib (actually a deliberate technique), and lace rib and cabled rib, and even faux ribbing. But we won't worry about those for now :-)

Anyway, after you're tired of doing ribbing, you'll want to switch and do stockinette for a few more rows to help transition for your decreases. To make this switch, start after you've finished a Row 2 of ribbing (so that when you start the next row, you're looking at a Row 1 section). Instead of knitting and purling, you'll just knit all the stitches. Then on the next row, purl all the stitches. And so on and so forth, for another inch or two.

Now we're ready to learn how to do decreases. At their most basic level, there are two types of single decreases ("single decreases" are any decreases where you turn two stitches into one): left-leaning (the SSK), and right-leaning (the k2tog). Think of them as slash marks on the keyboard: one type of decrease will make your stitch look like this: / and the other type will make it look like this: \ . There are also many ways to do these decreases - I'm just going to show you one way of each - the most common way.

This decrease: / is done by making a "knit two together" (and is abbreviated as "k2tog"). It's just what it sounds like - when you're ready to make the decrease, instead of knitting 1 stitch, you will actually grab the next TWO stitches on your left needle, and knit them both as though they were just one. Once you've finished the stitch, those TWO that were on your left needle will become ONE on your right.

This decrease: \ is done by making a "slip slip knit" (and is abbreviated as "ssk"). This is a bit more complicated. What you will do is slip one stitch "knitwise" (poke your right needle in as though you were going to knit the stitch, but instead of knitting it you just slide it over to the right needle), then do the same thing to the next stitch - slip it "knitwise" as well - do this to each stitch one at a time, not both at the same time! Once both stitches are on your right needle, then you'll poke the tip of your left needle into those stitches, and knit them together. This has the same - but also the opposite - effect of the "knit two together": you're turning two stitches into one, but in this case you will notice that instead of looking as though the finished stitch is leaning toward the right, now your stitch appears to lean to the left. This is important in achieving symmetry in shaping! (for example, the neckline of a sweater will have SSK's on the right side and K2tog's on the left, so that the columns of decreases lean becomingly away from each other, rather than haphazardly all the same direction.

Here are videos demonstrating each technique:
K2tog: http://www.youtube.com/watch?v=sBpbLmgwHFA
SSK: http://www.youtube.com/watch?v=RGwcYW3GG3M

OK, so here's what you should do, beginning on a right side row:

K3, ssk, K16, k2tog, K3

Now you should have 24 stitches on your needle, since you DECREASED two of them. Right? Yes.

Purl the next row as normal - decreases are generally (though not always) only done on right-side rows.

Next row:K4, ssk, K12 , k2tog, K4 (You should have 22 stitches now)

Purl the next row

Next row: K5, ssk, K8, k2tog, K5 (You should have 20 stitches now)

See what's happening? Your decreases are becoming visible on the right side (knit side) of your fabric, and they're starting to make a little pyramid shape! Like this:

  /      \
  /       \
 /        \

This is the same basic concept of how we will decrease stitches to shape the crown of your hat.

Carry on in this manner until you only have a few stitches left on your needle, and your pyramid is almost at its point - then I'll show you a double decrease :-)

HTH!
K