You're probably making one of the most common beginner mistakes--holding your working yarn up over the left needle and knitting into the two loops of the stitch below the first stitch when you start a new row. That will add one stitch to each row, so it grows wider quickly! If you make sure your working yarn is not over the top of the needle, you'll do better.
It's probably growing longer as well, but it seems to take forever when you're making it wider each time around.
There's also a "sticky" thread at the top of this board. Look here
for more information.
Also, be sure to watch the videos to get a better idea of how things look.