How one transposes is also a personal preference. Basically it breaks down two ways. You either tranpose intervalically or using clefs. Yes, there are exceptions, but most of us fall into one of these two groups. I fall into the interval group. I can read clefs, but I don't use them when transposing. And some transpostions are easier than others for me. Playing a C trumpet - F, A and Bb transposition are very easy for me where E, Eb and D do not flow as easily. It is strange....you would think if Bb is easy (down one step) that D would be just as easy (up a step), but sometimes I will be reading in D and suddenly slip to Bb. It is the way my brain is wired I guess and I rarely have to do "D" transposition. Playing piccolo and lots of orchestral literature F is a breeze (up a fourth) and of course being a C player, I can read Bb without many hiccups. I could go on with examples, but you get the idea.
The most famous book for this task is Sachse, Sachse, Sachse.....my most-hated book at one time. My lessons with Rapier always included a lot of these and in every key imaginable. He never told me how to transpose - that was left up to me. He would just say or write "this etude in E, Eb and A", etc. Also, transpose other etudes as well. Start with some easy books like Getchell and Bousquet. (In grad school we had to transpose all of the Charlier's!!! Oy vey!) It is a matter of making yourself do it. At first, it really is no fun, but you will love getting better at it. The best way to go about it is to play etudes VERY SLOWLY and DO NOT go on to the next note unless you are SURE of what it is. NO CHEATING!!
P.S. When learning to transpose, it is not a bad idea to go through the etude a few times with just your fingers and not waste valuable chop time. This is an efficient way to work your brain and fingers while resting the chops.