Build patio slabs at a slant to allow water to run away from the house. A mild slope of one-quarter inch prevents pooling of water on the patio and allows any dirt on the patio to wash away.
Keep the slab higher than the surrounding flower beds. If the patio is already built, you can achieve this by digging out the flower beds. Another solution is to frame the flower beds so soil doesn't splatter onto the patio slab. A frame slightly higher than the patio slab prevents an overflow of soil onto the concrete.
Plant grass around the patio and maintain it. This reduces the amount of soil and dirt around the patio.
Use sandbags when you need an immediate fix during a heavy rain. Line the patio with sandbags to prevent dirt and mud from overflowing onto the patio.
Use step stones, rugs and other items to create walkways to keep from tracking mud.