After you solve your basement's moisture problems, your main concern becomes the floor: Is it sound and level enough to finish with your floor-covering choice? If your floor shows no signs of moisture problems, is level (no high spots of more than 1/8 inch in 10 feet), and is not severely cracked, it may need only surface repairs before you install underlayment (in areas you intend to cover with vinyl flooring) or a finished floor. If the floor is badly cracked, broken, or damaged, you'll have to resurface it, either with self-leveling compound or new concrete.
First check the floor's surface for evenness by rotating a 6-foot level on the floor in sections. Mark dips or high spots with a carpenter's pencil. Repair those areas as follows:
Lows and Highs.
Fill depressions with patching compound, troweling them smooth and feathering them to the surrounding floor. Rent a concrete grinder to level high spots. Check the surface of your repairs with a straightedge, continuing to fill or grind until the floor is flat and level.
Cracks and Holes.
Use hydraulic cement to repair them.
White or yellow alkaline deposits impair adhesive bonding on glued-down floor coverings. To remove the deposits, mop the floor with a solution of four parts water and one part muriatic acid, then rinse the slab with clean water. Muriatic acid is extremely caustic, so follow package directions carefully.