Growing a healthy lawn with proper mowing and watering can keep weeds from sprouting. Here's how to go after the weeds you have:
Hand-weeding is still the best defense on small lawns where the number of weeds isn't overwhelming. It's most effective against annual broadleaf weeds. Pulling them while they're young—before they flower and seed—is the simplest way to prevent them from spreading.
Catching perennial weeds early is crucial. Dandelions, for example, develop deep taproots that are hard to pull once they mature. Yank the entire plant, including the root—any root pieces left underground will grow new plants. If new sprouts grow, pull them repeatedly to eventually starve and kill the weed.
Weeding is easiest when the soil is moist. Tools like the dandelion digger help get at the root by probing deep into the soil. Once the weed is out, promptly reseed the bare spot; otherwise, new weeds will fill it in.