It is surprising how much life is left in your garden from last year. If you let any plants go to seed, the seeds will be ready to sprout. Even if you didn’t, there is a good chance there are seeds that didn’t sprout that will grow this year; root vegetables that you missed when harvesting will enter their second year of growth.
Look closely at comes up and don’t be too quick to pull “weeds”. Most vegetables will sprout two dicotyledan leaves first. With experience (and a little help from google perhaps) you will be able to tell the weeds from the vegetables. For example, Russian kale has a purple tinge to the leaves and they are a bit fuzzy. Carrots have long thin grass like leaves. Potatoes are obvious, they look just like the sprouts old potatoes start growing when you leave them too long before eating. Lettuce is the hardest because so many weeds look similar. You may have to let some volunteers grow until they have a few more leaves to be sure what they are.
Root vegetables can either be eaten immediately before they use up too much of their stored energy or can be left where they are to produce seeds for next year. Potatoes will grow more potatoes. Other volunteers can be gently lifted, getting as much of the root as possible and transplanted where you want them.