You'll need a diode (or full-wave bridge rectifier) and a capacitor. [u]Here[/u] is some information I just found about building power supplies. (I've built lots of power supplies, but I just did a search to find some sample schematics.)
The capacitor will charge-up to the AC peak which is about 1.4 times the RMS voltage. So a 12V AC transformer will give you about 17V DC. You'll get a 0.7V drop across a single diode, or twice that across a bridge rectifier. But with a light load, you'll probably get more than 12V out of the transformer so I wouldn't be surprised if you get 20VDC. Do you have a multimeter?