I think Elizabeth's question has probably been answered, but if not, in a very barebones sense, there are two big categories of annual plants based on whether or not they'll die in a frost. Lots of common garden plants (including tomatoes, peppers, eggplants, basil, sweet potatoes, summer squash, winter squash, and cucumbers) will die if you get a frost, so you need to wait to plant them out until after the last frost of the spring (you can often transplant them to hurry them along), and you should try to get them all harvested before the first frost of the fall. These crops will generally refer to the frost on the seed packet and say something like "Transplant after all threat of frost has passed."
The other big category is plants that will survive a mild frost, including lettuce, mustard greens, kale, chard, collards, broccoli, cabbage, cauliflower, carrots, beets, onions, turnips, rutabagas, peas, and potatoes. That doesn't mean you want to plant them outdoors in the middle of winter, but you can get away with planting them when the ground has thawed out in the spring and you're unlikely to see many nights below 25 F or so. Seed packets will often list this as "plant in spring as soon as the ground can be worked." If you're using a no-till garden system, you may not have to do any "working" at all, so just make sure the soil isn't frozen and is also not completely waterlogged - if you can turn it over with a shovel and the soil you dig up can't be wrung out like a dirty dishrag, you're fine.
Here in southern Pennsylvania, I can generally plant my first outdoor crops between March 15 and April 15. It depends on the year - sometimes we have three feet of snow on the ground in early April, and sometimes it feels balmy and tropical in mid-March. I won't spend a lot of time planting if the 10-day forecast shows a lot of chilly nights and a high chance of snow, but I know that we're very unlikely to get a low in the teens by this point. Where the equivalent spot would be for you depends on your climate - in southern Virginia, you might have greens planted out by mid-February, but in Wisconsin the ground might still be frozen solid on April 1st.
There are some more complex cases (for instance, you can harvest field corn in the depths of winter, but around here you can't plant till mid-May), but in general, when something says "plant in spring", it means "once you can turn over a shovelful of soil and not find it full of ice chunks or completely saturated with water, go ahead and plant it".