How you repair a leaky foundation wall depends on what type of material the foundation is constructed. Masonry and concrete in most cases can be quickly and easily patched. Stone foundations often require extensive repairs or replacement.
Small cracks in a masonry foundation often occur from ground settlement or earth shifting, too rapid a drying of the mortar between courses of block when installed and even excess ground water can exert sufficient pressure on the exterior to crack a wall.
First examine the interior and exterior of the foundation wall to see if there is a physical reason the wall is cracking. If the earth alongside the foundation has sunken due to missing downspout leaders adding tons of water against the foundation or perhaps the grade has been changed without someone realizing that rain water is now flowing up against the building.
Ponding water can super saturate soils causing them to sink and exert thousands of pounds of pressure to adjacent objects such as a foundation wall. Since a basement is back filled on only one side and is open air space on the inside, this hydraulic ground pressure can easily crack a masonry wall and may with time crack a solid concrete foundation as well.
Your first action should be to correct this problem by re-grading or other necessary work to assure all water runs away from the foundation. Once done, turn your attention to the foundation itself. Minor cracking occurs in all walls over time and if no inward bowing of the wall is evident it indicates a simple shrinkage crack has occurred in most cases.
Using a small four inch electric grinder with a masonry blade (always wear eye and ear protection as well as a dust mask) carefully grind out the masonry joints between the blocks or cut into the concrete crack perhaps a good inch or more. Do not cut more than two inches deep to avoid cutting any rebar in the concrete wall. Once the grinding is done and the dust has settled, remove all traces of dust with your shop vac making sure the cracks are clean inside as well.
If you are working on a masonry foundation mix some new mortar making it fairly loose and pliable. Using a brush or spray bottle thoroughly wet the blocks with plain water along the entire crack itself. If the blocks are too dry they will suck all the water out of the new mortar and dry it too quickly causing the mortar to fail.
The mortar will simply pull away from the blocks leaving a new crack. You want the new mortar to dry as slowly as possible. Concrete foundations are handled differently. There are a number of concrete crack sealants on the market today that are used to inject into a concrete crack and seal it.
Most can be installed with the use of a standard caulking gun. When injecting the caulk, fill the new void completely but try to leave it just a hair below the surface of the wall when finished. The sealer will air dry itself and needs no additional work.
Once all cracks have been repaired and completely dried the application of a good masonry sealer can be painted on the inside surface to further waterproof the foundation. Always make sure you paint the wall higher than the exterior grade elevation and paint down to floor and out onto the floor itself at least three inches to assure a good seal at the wall to floor joint.
Masonry sealers work on both masonry and concrete walls and come in various colors. Application is done with simple paint brushes and heavy nap rollers. No special tools are required.