older computer
 

I have Windows 98 and I'm wondering if I can download a program that lets me burn cds. This computer doesn't have a cd burner in it.

There are plenty of programs out there that can burn a cd but you can't burn one with out a cd burner. You should be able to get one fairly cheap and most should work with windows 98. Try searching on google.

Most burners will come bundles with burning software, otherwise there a few few freeware ones around. Try www.doom9.org, look at their software download page.