While the term weed is usually used to mean an undesirable plant, it is often location specific. Some plants considered weeds--dandelions, for example--are also used for commercial purposes. Trees can be considered weeds if they are growing in an area you don't want them to grow. Most trees and weeds, however, are easily distinguishable. If you come across a plant you aren't sure of, don't pull it out until you know if it's a tree or a weed.
Look at the base of the plant. If there is a woody stem, the plant is probably a tree. If there is a thick green stem, the plant is probably a weed.
Examine the leaves on the plant. Small trees will have leaves at the end of the branches that are the same shape as the tree when it is fully grown. Weeds have large or small leaves on the main stalk that usually fan out.
Check the location of the plant. Trees usually grow where there are similar trees nearby. If a tree of the same type is growing close by, the plant could be a tree. If there are no trees of that sort growing close by, the plant may be a weed.