Condoms are very good at protecting against most STDs (not all--they do not protect against herpes, which is transmitted via skin contact) and pregnancy. Ensure the condoms are the right size (not too loose or tight). Do not use two condoms at once. Make sure it hasn't gone past the expiry date. Put it on correctly (there should be instructions. It's quite easy. Make sure the "rim" part is out, pinch the tip, and roll it down). Make sure neither of you carry condoms in your wallet--the friction causes microtears which damage the condoms and lower their effectiveness. Use lubrication with condoms, even if they're pre-lubed. Spermicidal condoms are not any more or less effective than regular ones.
You could also both get tested for STDs (including a blood draw--that's how you test for herpes, which is the most common STD), and you could ask for birth control medication from your doctor.