As a general rule of thumb, when the soil is warm enough to be growing weeds then it’s time to sow all manner of vegetables outside, which will normally be from late March to the beginning of April.
The best time to remove these weeds is when they have reached a good size and you can use several methods to get rid of them. You can either pull/dig them up, hoe, burn with a small flame gun or spray them.
Many of the weedkillers designed to control weeds are systemic, such as Roundup or Weedol, work by being absorbed by the leaf into the sap systems where it travels around the weed and taken down to the root, so the weeds can’t grow back. If soil temperatures are still quite low then these types of weedkillers can take several weeks before they show their full results - but that doesn’t mean you have to put your plant growing plans on hold.
Make sure if you are choosing to go down the route of spraying with a weedkiller when your edibles are already growing, that you either cover them with plastic or shield them with a piece of cardboard so no spray drift gets on them.
Both Roundup and Weedol Rootkill Plus are inactivated on contact with the soil and are then broken down by micro-organisms to allow re-planting. So even before the weed has been killed off completely you can start cultivating the treated area.
The first photo below shows a trench where a row of potatoes is going to be planted. You can still see the weeds that were sprayed with a weedkiller a week before the trench was dug. Although they’re not completely dead, at this stage, there are obvious signs that the weedkiller is starting to work so you can proceed with planting the potatoes even before the weeds are totally dead.