When you start grooming a horse, you'll want to use a currycomb first. This will help loosen up the dirt and hair, which will make it much easier to brush away.
The picture below will introduce you to what currycombs looks like:
If you are new to grooming horses, you may not know which one to use. There are basically three types:
To start, if you are using a plastic or rubber variety you'll start grooming in a circular motion. A good place to start is at the top of the neck, just behind the head.
Begin at the top of the neck and work your way to the barrel, back, and legs.
When working on grooming a horse, there are a couple ways you can move along in the process. For simplicity's sake in this tutorial I am showing using only this brush first, followed by a soft brush after completing one side. Another option would be to put a soft brush in the other hand and work in small sections.
Here you can see special notice being given to the area where the girth or cinch of the saddle will be. If there is a lot of loose hair and dirt, it can cause a cinch or gall sore. They are painful and can make it so you can't saddle him for awhile until it heals.
This picture show the legs being groomed. Some horses are sensitive around their legs, bellies, and flanks, so be aware when cleaning these areas up.
Then you'll continue on working your way all the way back to the rump and back legs.
Once you've rubbed and curried with enough effort to have all the dirt loosened, it's time to move on to the next step which is soft brushing.