Here's a video tutorial discussing how to paint dirt in photoshop, specifically the technique of painting dirt in with a large texture brush, then painting out (erasing) with a smaller texture brush. The same theory works for digital rough paintings and speed paintings, but for this example I'm using the technique to show painting dirt for a texture map.

Here's some notes:

• When painting dirt, your first inclination might be to paint the dirt with a small brush. But this takes a lot of time.
  
• Your second inclination will be to use a large dirt brush, but that will likely add too much dirt to the painting.
  
• Your third try might be take the same brush and make it smaller. There's now less dirt, but the dirt will likely look too even.
• So the best solution is to Paint In the dirt with the big dirt brush, then Erase parts of the dirt to shape it with the same brush just smaller.
• Same applies to adding drips. Painting a drip with a single brush stroke will leave the tip of the drip too even, even with pressure sensitivity turned on. So paint in the drip with your bigger brush, then use a smaller brush to erase the tip of the drip to create a nice sharp point.
• Then feel free to use a smaller brush to add a few details.
  

Here's the final result: