The fix for a wet basement depends on how the water gets in. Water seeping through a wall in one spot often points to a crack or a gap around a pipe. Water appearing along the whole base of the wall, or rising through the floor, points to groundwater pressing on the foundation from below and the sides.
For the second kind, the standard repair is an interior perimeter drain: a channel cut into the floor along the walls, pipe set in stone, and a sump pump to carry the water out. Some jobs are better done from outside by excavating along the foundation and sealing the wall, which costs more but keeps water out of the wall itself. Ask any company you talk to why it recommends one approach over the other for your house, and get the scope, the warranty and the total price in writing before work begins.