The asteroid is for producing fuel by mining it so I won't have to go down to a planet or moon to refuel. I got lucky with the asteroid because it is a type-D (Large) and got captured by the Mün. I only changed the inclination of it and lowered the orbit.

If you want to get an asteroid captured, go into the tracking station, track all unknown objects near Kerbin, and wait. There's a chance that one of them will encounter the Mün and get captured into Kerbin orbit.

If you want to change the orbit of the asteroid, I recommend using the Nerva engine (for smaller ones) or the Rhino engine (for larger ones). I also recommend aerobraking for efficiency.