Choose a piece of music which you know well. Pick a section to use to practise your transposition. Look at the key signature and work out what key this section of music is in. Next pick a new key that you will transpose the music into.
Take some manuscript paper and on it write down the new key signature. Then work out the distance between the new key and the old key (the number of tones or semi-tones). You can mow work your way through the music moving all the notes by the distance you just worked out.
Finally when you have finshed writing take your new piece of music to your instrument and try to play it.
Do this exercise regularly and it will gradually become easier – when you become really advanced you will be able to do this straight on your instrument without any manuscript paper at all.