You can transplant it anytime of the year but the best time is during the spring where the plant resumes to grow. But if you decide to transplant it, the plant would go through shock until it resumes growth.
Just replant the plant in the soil that originally grew in.
Why do you want to transplant it?
If its doing well I wouldn't mess with it since replanting can put the plant into shock.
But if you insist on doing it I recommend popping the plant and the dirt (soil or medium, whatever you wanna call it) all out at once so you don't disturb the roots then put the whole thing in a new pot.
I usually use 60% peat ~ 40% perlite. some do 50~50 or mix sand instead of perlite. Personally I dont like using sand its too darn heavy and I cant help but think that its squooshing the roots