QUOTE(jo.clarinet @ Jan 15 2006, 08:08 PM)

The way I always teach it to my pupils who are doing Grade 5 theory is the following:
1. It doesn't matter at all whether the original piece is in the major or minor - look at the key signature and decide which MAJOR key it would be (pupils are often more reliable on their major key signatures than on the minors!). Then from that keynote go down/up the required interval. Take that new note as the tonic of your new major key and put in the key signature.
eg. if the key sig is 2 flats and you are asked to go down by a minor 3rd: the original key sig is that of Bb major. Down a minor 3rd from Bb gives you a G, so your new key sig is that of G major, ie 1 sharp.
2. Write all the notes down or up the required numerical interval, ignoring the notes with accidentals for the moment.
3. THEN deal with every note that has an accidental, raising or lowering it as was done in relation to the key signature in the original. Some of them may be just 'reminding' accidentals, but they should be put in nonetheless.
This sounds complicated when written down, but is a pretty straightforward way of doing it!
1) I do same as jo clarinet for this.
2) I tell mine: if the transposition is a major 2nd, the notes on lines will go to the next space, or notes on spaces to the next line; if the transposition is a minor 3rd, notes on spaces go to the next space, lines to the next line; for a perfect 5th, lines to the next but one line, spaces to the next but one space. Ignore the accidentals for now. This is the same as moving the note a 2nd, 3rd or 5th and is very quick to do.
3) Deal with the accidentals last. I suggest that they count semitones for this: 2 semitones for a major 2nd, 3 semitones for a minor 3rd, 7 for a perfect 5th. If the original has an accidental, the transposed one has an accidental too.
Seems to work. They get it very quickly and don't often go wrong