Use a hoe (which is a sharp blade fixed to a handle) to slice off seedling weeds just below the soil level. The decapitated seedlings will then wilt and die as the roots are unable to re-grow. Frequent hoeing when seedlings are small is most effective. The hoe blade should run parallel with the ground just skimming the surface.
Avoid hoeing perennial weeds which will re-grow from fragments of root. Instead loosen the soil with a fork and left them out.
Keep the hoe blade sharp at all times. It is best to hoe when it is sunny and the soil is pale and dry. Don't hoe when the ground is wet.