When you first create an XBox 360 profile, there are only a few pictures to choose from. You can download TONS more from XBox 360 Live.
First, use the X button on the center of your controller to get into your profile area. Choose your profile, or create a new one if you don't have one yet. Now press Y to get to the dashboard.
Gamer pictures on your XBox hard drive are available to all profiles - so you only have to download them once. Go to the XBox Live tab - the one on the far left. Choose the XBox Live Marketplace. Now click the THEMES / PICTURES link.
Note that MOST of the pictures in here cost cash. Well, they cost "points" - which you have to buy for cash. So for example getting a Boston Celtics picture set is 150 points, so about $1.50. It's not a lot of money really. There are a TON of pictures in here. There are pictures for each NBA team, each NFL team, each soccer team, plus a bunch for various games. Be sure to look for FREE ones that appear in here occasionally - especially around certain holidays.
Once you have downloaded the pictures you're interested in, it's time to use them.
To choose a theme for your profile, hit the center X button on your controller to bring up your dashboard. Do this even if you're already in a menu. Go down to the top entry - the one with your current picture and score.
On the next menu, click on the second link - edit gamer profile.
On this page is the Gamer Picture link. Choose the "change" option, and select the new picture you want to use!
This is seen by any of your online partners when you're selecting up games with them, if they choose to look at your details.