I just had two toenails removed, what's the best way to prevent infection?

Keep it clean. Follow the instructions the dr. Gave you.
Keep Clean. The best thing to do is to keep the area clean. Putting some neosporin and a bandaid on should help if a bandage is not already on from the physician. Change the bandage around twice a day. Avoid tight fitting shoes as well. http://www.drugs.com/cg/toenail-fingernail-removal-aftercare-instructions.html.
Nail. Clean with sterile water twice a day. This will scub and remove crust which can be a nidus for bacteria infection. Keep it covered while still oozing.