“Transposing” means to put a tune into a different key (usually for ease of playing or singing, or for the purpose of playing with other instruments). As others have mentioned already, it’s not a worry if you want to play a tune you already know on, say, a D whistle on a C whistle instead…you use the same fingering you always do, and the whistle will take care of the transposing for you.
A little “cheat” for you…if I have a tune written in C and I want to play it on a D whistle, I just “pretend” that the bell note on my whistle is actually middle C and read the music accordingly
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Outside of whistle-switching, learning to transpose on paper or by ear takes practice and a basic understanding of the relationship of notes within a scale. A scale is made up of whole steps and half steps between the notes, and all major scales follow the same pattern:
whole|whole|half|whole|whole|whole|half
It’s easiest to envision if you look at the keys on a piano. White and black keys, right? OK…when two white keys are separated by a black key, there’s a whole step between them. When they aren’t, there’s a half step between them. So, if you play a scale in C (starting on middle C), you’ll take a whole step from C to D, another whole step from D to E, then a half step from E to F, a whole from F to G, a whole from G to A, a whole from A to B and then a half from B to C.
Still with me?
When you’re playing a major scale in C, you don’t need to write in any sharps or flats. But what if you want to play a major scale in D? If you just shift your fingers up a note and try playing on just the white keys, it doesn’t work…the spaces (“intervals”) between the notes aren’t right. You start by moving from D to E…that’s a whole step and it works fine. But the interval between E and F is a half step and you need a whole step here. So you play the black key next to F (F#). Next you play the next white key (G) because the interval between F# and G is a half step, which is what you want here. You continue on up the white keys on the keyboard until you run into another problem…the interval between B and C is another half step and you need a whole…so you play the black key next to C (C#).
So the trick in transposing music lies in knowing which notes must be sharp or flat to produce the appropriate scale. Transposing among majors isn’t too hard, if you keep the image of a piano keyboard in mind…minor scales are a different ballgame because a minor scale uses different intervals.
If you want a book that will lay all this out for you and give you a handy reference, there is actually a “Music Theory for Dummies” (or perhaps it’s “The Idiot’s Guide to Music Theory” (which, like most of the “Dummies” and “Idiots” books, isn’t for dummies or idiots at all, but simply spells out things in plain language for those of us who don’t have years to devote to studying such things
). It even has a chart that shows you all the key signatures (i.e., requisite sharps and flats) for both major and minor keys…useful if you actually want to do some transposition on your own. Probably not a problem you’ll run into a lot on the whistle because you DO have the option, quite often, of just switching whistles and using your regular fingering, but handy if you have a D whistle and someone wants you to play something you normally play in D in G or A.
Does that help at all, or just confuse matters further? I must admit that theory has never been my strong suit…I even had to run down to my piano to remind myself of the proper intervals for a major scale just now! 
Redwolf