You're not clear with your set-up, but if your computer is directly connected to your DSL or cable "modem" and that's the only piece of equipment you have, you can add a router (wireless or otherwise). This does NOT replace the ISP's "modem" (it's technically a router - the term "modem" was to allow people years ago from the old dial-up days to easily identify the box). To add a router is simple - unplug the cable that comes from the ISP's "modem" that is attached to your computer, and you plug this into the "INTERNET" or "WAN" port on the new router you purchase. Then you plug your computer into one of the existing numbered ports on the router.
Most routers are configured to work straight out of the box. It will require minimal configuration if you have a DSL connection.
If your ISP has provided both a "modem" and their own router, you should be able to replace the router they supplied. But if I had to guess, it sounds as if your computer currently is directly connected to one single box. Hope this helps. There are many different routers available - units from D-Link & Linksys are the most popular. You won't go wrong with either manufacturer, however, I find the configuration screens on the Linksys to be less "clunky." There are other brands you can choose from, too. I have less experience with these, but it doesn't mean these products aren't as good. Additionally, you can often find deals on cable/dsl modems all the time.
One piece of advice: Once you have the new router set-up & you're satisfied with it, check for a newer firmware update. Not all routers come with the latest firmware, and having the latest firmware installed insures you will have the most protection & best performance available. You'll be up & running in a matter of minutes, and it will not "break" your internet connection.