Best Method to Apply Pigments to Tank Treads?

Mix the powder in a small drop of water with a tiny drop of washing up liquid. But you will be hard pushed to get as good results with pastels as you will with pigments.

Bish's method works well.  

Another method that works well for caked on dirt:  

Mix 50/50 water and white (school) glue.  Apply the mix to the area that you want some build-up of dirt or mud.  Use an old brush to stipple or smear the ground pastel onto the model.  I recommend first trying the method on a piece of scrap or on the underside of the hull.    

Several options are available. Mig and AK make a pigment fixer, which is similar to a clear coat. Another option is using a varnish, an acrylic paint medium, or even Humbrol's Decal Fix. You can either apply the fixer to the model before you apply the pastels, or after, or even mix them together. Look at this video from Humbrol for a good rundown on technique.

I've used water and acrylic thinner as a "fixative," but the adhesion was poor (although better than nothing).

I have used both pastels and the expensive weathering pigments/powders from AK and Vallejo. I cannot tell the difference. I use the cheap chalk pastels, not the high-end artist type. Craft stores sell a pack of 12 earth tones which cost less than $15 US. I grind them with sandpaper, or if I really need a fine powder, I'll use a mortar and pestle.

I use Vallejo's Medium Thinner. I mix in their light yellow ochre pigment and apply it like a wash. While it's still wet I brush on natural umber pigment. When it's all dry I use a stiff brush to remove some of the pigments from the track contact points and dry brush a steel color over the parts that contact the ground. All this results in a dried mud effect. I have the Vallejo Mud and Sand pigment set. It only cost about $7.50 for a set of four 30ml jars. The white glue and water mix mentioned above works fine, but since I discovered my little method I like it better. If you're trying to save money though, the white glue/water and pastel chalks should work OK.