There are all the usual options: mulch (deep layers of organics like hay, straw, leaves, etc. or thin layers of light blocking things like plastic or paper sheet mulches), and mechanical removal methods (hoes, hand pulling, flaming), and of course chemicals. They all have their pros and cons. Organic mulches can add good to your soil, but might bring other seeds with them, plus may not be easy to come by depending on where you live. Plastic needs to be removed again, and disposed of. Mechanical removal is best done when the weeds are very small, but tends to take constant vigilence. You get the idea. This year I am going to try a combination of paper mulch (designed for the purpose), and hay/straw. I had good luck with cardboard under hay last year, but it was hard to get my hands on 200 boxes. Not to mention installation was a drag.

I don't know how long you have until your last frost and will be planting ... but I'd cover the beds now with cardboard boxes. Keep them in place with landscape tacks and you'll likely be able to kill many weeds that try to peek out. I put cardboard down in my zone 8 beds in early January (which also had weeds because of too much work travel last fall!) and I have no weeds now. Doesn't mean there aren't any lurking seeds just waiting for some sunshine, but I took some cardboard off for about 10 days during a recent warm spell and nothing sprouted.

Once you plant transplants mulch well to keep those weeds down ... and hope that your seed-planted beds have a fighting chance. Good luck!

I have used black plastic for the last 4 years and do not have a weed problem.
Till the ground in the fall, cover with black plastic while it's still warm. The seeds sprout but fail to get any height as the lack of light knocks them down again.
It is also very helpful with compaction. I can pull the plastic in the spring and sow straight in without turning the soil again. A good time saver.

Fertilize and water the empty beds. Weeds hate fertilizer and water. Then mulch heavily with compost using a layer of newspaper or cardboard under the compost. This is also the easiest way to start a new bed IMHO. Even over grass here in the northern west central region.