I'm starting to teach myself how to crochet from a book. My problem is that when I try to make the next row I can't understand how to do it properly. The sides are not even. It looks like I'm either gaining or losing rows. What am I doing wrong?

I do that, every time I pick crochet up after not doing it for a while...

So you make a row... then chain 2 (or MORE if you are doing double stitches) Then flip it and insert the hook in the second from last on on the first row.... The chain you just made has to take the place of one stitch.

I usually do a 15 stitch square just to get the hang of it again, because I usually stick it in the wrong stitch, and gaining a row

Also, try and watch your tension on the first chain stitching, if its too tight it will "pull" your first row, tight making the rest of the stiches look looser.

Hope that helps... good luck, teaching yourself is sometimes harder, cause there is no one right there to ask.