As mentioned if you test you will always find mold. First thing is to address the cause - mitigating moisture. Look into buying a dehumidifier - Amazon sells a very good one priced around $300 - I got one for my basement and it has done a wonderful job at drying it out. No more musty smell in my basement. Secondly if you can see it on your walls, mix some water and bleach in a spray bottle (2 parts water, 1 part bleach) and spray the spots. If your drywall is effected and soaked, the wet part will have to be cut out, but if it's just superficial hit them with the bleach. let it dry and Kilz it.
Grading can certainly help, but if your water table is high and you notice a lot of weeping from your unfinished walls, it's likely cause by the hydrostatic pressure against your foundation walls and this could exist regardless of your grading situtation. One of the most effective ways to deal with hydrostatic pressure is to relieve the pressure. You do this by trenching the inside floor around the perimeter (basically a French drain on the inside) and drilling weep holes that drain to the trench and then to our sump. Between a dehumidifier, trenching and making sure the grading around your foundation slopes AWAY from your house, your basement should effectively stay dry.
Grading can certainly help, but if your water table is high and you notice a lot of weeping from your unfinished walls, it's likely cause by the hydrostatic pressure against your foundation walls and this could exist regardless of your grading situtation. One of the most effective ways to deal with hydrostatic pressure is to relieve the pressure. You do this by trenching the inside floor around the perimeter (basically a French drain on the inside) and drilling weep holes that drain to the trench and then to our sump. Between a dehumidifier, trenching and making sure the grading around your foundation slopes AWAY from your house, your basement should effectively stay dry.