Pretty easy really...
There are different 'flavours' (sorry, flavors!) of wireless, each one generally better than the last. You will need at least the 'g' version of wireless, although different manufacturers have their own proprietary systems for upping range and speed beyond that basic level. BE CAREFUL - these proprietary systems do indeed increase range and speed, but often are not compatible with each other.
First of all, you need to ensure that your laptop is equipped with wireless!! If you're not sure, check the manual. If it's a recent model, it probably has a 'g' adapter built in. If so, you can get a combined ADSL/router and just connect that way. If you have no wireless facility in your laptop, or you need to increase the range over the standard 'g' speed, you'll need to get a wireless adapter for the laptop - most are PC cards that slot in, leaving an arial 'stub' sticking out. Often, you can get router/PC card bundles and save a few pennies.
The choice of router is down to you - for years I used Netgear, but finally gave up on them because of flaky connections. I switched to Linksys and haven't looked back. There ARE significant differences in performance between models - check out web reviews for comparisons.
A couple of points to remember:
1) Ensure the unit is a combined ADSL modem/router - many are router only and won't be a 'one box' solution
2) Make sure you know your login details to AOL - you'll need them to configure the router (usually done by connecting via an Ethernet cable)
3) After you have configured the router and can connect to the internet, enable the security!!!!!!!!! This means changing a few settings in the router and on your laptop - it's not too difficult, just be methodical. Try using the 'WPA' security settings as they are more robust than the older 'WEP' option.
Good luck - once you have tried wireless, I doubt you'll go back to wires...