If the leak is small (a couple pinholes) or otherwise contained (a crack in a relatively flat spot) then you can patch it with some repair epoxy. A tube costs about $5.99 at the auto parts store. They make repair epoxies for plastic and metal on radiators, and both are meant for this application.
It's really easy to do. First, clean the area with 100% mineral spirits in a microfiber cloth, then take some 400-grit sandpaper and scuff the surface a little. This will give the epoxy a nice rough surface to grab onto. Then clean the area again with mineral spirits, wipe it down with a dry microfiber cloth, and let it dry for a few hours in sunlight.
After it's dry, pull out your repair epoxy and mix it up according to the instructions on the tube. Then just apply it liberally over the leak; make sure you use a good bit. Try to sculpt it like a proper patch so that it covers a wide area in and around the leak. After you've got it pretty much sculpted the way you want, take the palm of your hand and beat on it a bunch to flatten it. This will push it against the area and make it grab tighter and seal better.
After you're done with the repair leave it alone for about an hour to set up. After an hour, pop the hood, crank up the car, and have someone rev the engine while you check the patch. If it's not leaking when the engine is at high RPM that means you're good to go. The repair epoxy will be fully hardened after 24 hours. If it IS leaking after an hour, sand down the specific area it's leaking from on the patch and add a little more epoxy to that area, or just chisel the patch off with a flathead screwdriver and try again.
This takes an afternoon and about 20 minutes of actual work and it only costs $6 to try, compared to buying a new radiator at ~$80 and spending a couple hours of actual work swapping them. And if the patch just won't hold, you can always buy a new radiator and you're only out $6.