Those green hitchhikers
The wonderful thing about growing in containers is that weeding is far less of a chore than with backyard gardening. If you can tell the difference between the weed and the plant that you're actually trying to grow - pull up the weed when it is small. If you're scared that what you think might be a weed is actually your plant - wait until it gets big enough for you to be sure, then use scissors to cut it at the base so you don't disturb the roots of the other plants.
To avoid the seeds from last year's plants becoming this year's weeds, throw away the soil when you replant the pot, and thoroughly clean out and sterilize your containers.