The first thing to do is to use a cultivator to remove as many of the weeds as possible. If there are perennial weeds in the same area, they will need to be dug, to eliminate their roots. Rake the area smooth, but hold off on adding any mulch for at least a week or two. This waiting time will allow for a lot more of the dormant seeds to sprout, and be easily removed. After the first initial flushes of weedlings, you should apply a good mulch layer over the soil, which will help prevent future weed sprouts.
Organic mulches are the best overall choice because they help build a healthy soil.
However, in some cases it is more advantageous to use black plastic or a weed blocker fabric. At this point, you will now have a reasonable amount of control over any annual weeds in this garden. From this time on, however, vigilence will be critical, to ensure that any further weedlings that sprout are immediately removed before they have a chance to flower . Just a few rogue weeds that survive to flower and reproduce, can undo a lot of your best efforts. You will have to keep working at it, until all of the weed seeds which are laying dormant in the soil have sprouted, and the resulting weed removed.