Brushes are especially popular in jazz music as a tool that gives many sound possibilities.
I will discuss the basic techniques of "scraping" with brushes that are worth improving when practicing on a snare drum, because they also increase the efficiency of our hands.
1.Keeping the time - left / right
Start by moving the left hand brush (if you are right-handed) over the snare, moving the brush in a rhythmic way - to start with eight ("1" from right to left, "and" from left to right, "2" from right to left, "and "from left ti right, etc.).
Your right hand can tap quarter notes, eighths or "scrape" in the opposite direction during this time, i.e. when the left hand moves from left to right, the right hand moves from right to left.
In this way you can play the basis of the jazz rhythm of "swing" - the left plays the aforementioned Eights, and the right hits the snare drum, playing the swing figure (quarter notes on 1 and 3 and shuffle figure on 2 and 4).
Eights played this way with the left hand can be shifted relative to the main note, i.e. when you count "1 2 3 4", you can move the left exactly to the main note (1 2 3 4), or, for example, one eight note triplet after the main note ( then the main note, i.e. 1 2 3 4 and a brush moving along the snare, create the rhythm of the shuffle figure).
Listen on YouTube how eminent jazz drummers do it, e.g. one of the masters playing with brushes - Ed Thigpen.
This is the second popular way of playing with brushes. It consists of "scraping" with brushes in a circular manner, ie one hand or both rolls in circles, usually in the opposite direction (when both at once).
Start with the left hand (if you are right-handed) - the brush makes a small circle, from the outside of the snare to the inside, but beware - the duration of such a lap is not accidental. At the beginning count with quarter notes, i.e. counting "1 2 3 4" you make four such circles with your left hand.
When you feel free to circle left, add your right hand. Start by hitting the quarter notes played on the right on the opposite side of the snare with the left hand, which circles.
In the second stage, try playing the "swing" figure with your right hand while the left one makes circles.
With the right you can also turn the wheels the other way - also from the outside to the center of the snare, or turn large half circles, from one side the snare to the other (one half right circle when the left one makes a smaller circle).
There are many techniques for playing with brushes, it is impossible to discuss them all, but it is worth starting with the few simplest, though not at all easy. I encourage you to learn more brush techniques.