Weeding by hand is all well and good, but special gardening tools make the work much easier and are often much more effective. Root weeds such as dandelion, sorrel, goutweed or bindweed must be thoroughly removed with roots, otherwise they will spread quickly again.
You should remove the weeds as early as possible in their growing season before they can spread via seeds or runners. It is easier to weed if the soil is slightly moist or if you loosen the soil beforehand with a digging fork.