Here is how "Granny" made a quick and simple crocheted blanket. It is something most beginners can learn quickly, as the technique is the same for each row. Using Granny squares, you can crochet a blanket without having to carry the blanket-in-progress with you. You make the squares individually, then stitch them together.
Step 1

Obtain yarn of your choice.
Step 2
Obtain an appropriately sized crochet hook.
Step 3

Chain six. Form a slip knot around the hook, wrap yarn around the hook, and pull it through the loop in the knot. Now the yarn that you pulled through is wrapped around the hook, and you can pull another loop through that. Be sure to leave a little extra yarn at the beginning in case it is needed later.
Step 4

Slip stitch into first chain (to form a ring). Pull a new loop through the loop that's already on the hook, as well as through the chain stitch.
Step 5

Chain three (equivalent of a first stitch of double).
Step 6

Make three double crochet into the center of the ring.
Step 7
Chain two.
Step 8
Make three double crochet into the center of the ring.
Step 9
Chain two.
Step 10
Repeat two more times, for a total of 4 groups of 3 dc (double crochet).
Step 11

Slip stitch into the top of the three chain to finish the round.
Step 12

Add a new color for the next row if you like... simply start crocheting with the new color.
Step 13
Chain three (an equivalent of a first double crochet).
Step 14

In the "corner," one of the spaces created by the chain two between sets of double, do 3 double, chain two, and three more double. This begins to create the square.
Step 15

Chain two to the next corner, and repeat. Do all 4 corners, and then slip stitch to the first corner to finish the round. Each corner should have two sets of three dc, each separated by two chain stitches.
Step 16

Change colors again if you like.
Step 17

Double crochet TWO bunches of three (separated by two chain stitches) into each corner... but only ONE bunch of three dc into each "flat side" hole from here on out.
Step 18
Continue for as many rounds as you want. The number of side spaces will continue to increase. You can make a potholder by backing your square with sturdy cloth, an ornamental doily with a thinner yarn, or even a baby blanket. Sew multiple squares together to make an afghan.