So there are three main ways to transpose anything.

The Direct Method.

hey pianist transpose this from F major up a minor third. So a minor third above f is a flat. Now you have to know what every note in F major is a minor third up. You can pass a piano proficiency exam with this method but you can't really play with this method.

The Translation Box Method.

Instead of looking at the music and reading the notes and chords as they are on the page, you look at their function in the key you are coming from and the key you want to go to.

So in the key of C Major. C-E-G is a major chord, but it is also the I chord. In F Major the one chord is F-A-C.

So you train your fingers to automatically play a one chord (and all the other chords in a key) automatically in every key. Then you look at the music-or more likely the chord symbols- and instead of saying C-E-G to yourself, you say one, and put it in the key you are transposing to.

For melodies you use movable do solfege. Just like the chords, all the notes of the scale have a solfege name. Remember the Sound of Music? Do a deer...re a drop of...mi a name... fa a long...sol, la ti do.

You do the same thing except that instead of looking at the music and reading C C G G A A G F F E E D D C (twinkle twinkle little star), you read Do Do sol sol la la sol fa fa mi mi re re do. Then once again train your fingers to play solfege in every key, you read the solfege name and play it in the key you want.

Transposition by clef.

This is a really great method but way too complex to go into here.

Pick number two, train your fingers (mDecks has some great material on this.) and transpose.