For example, suppose you know how to play in the key of G which mainly uses G, C & D chords with an occasional Em and Am. (Which chords you use is often based on the Circle of Fifths aspect of music theory). Now you see a song you'd like to play in a song book but it's in the key of E. You can easily convert it to G by moving every note and/or chord up three frets (or one and one-half steps).
So every E would turn into a G (E F F# G),
You can write these chords in place of the original ones and play the song in the key of G now.
And if you want to play it in E, you can put a capo on the 9th fret. Some folks regard this as cheating; I think of it as a learning situation. Eventually, you ought to be able to play in several common keys, but there are certain chords that sound better for certain songs and you'll want to use a capo on a guitar or banjo or dobro to make the instrument sound just right.
Here is a transposition chart to get you started.
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You can convert any common key to any other common key using this chart. Just choose the row of the key the song is written in and choose another row of the key you want to convert it to. Then whenever you find a chord in the first row, simply replace it with the chord from the same column in the second row. If the original chord is a minor (m) or 7th or some other extended chord, just add that information to the new chord.
A far easier way to transpose is to use the Nashville Notation where every chord is given a number based on the key you're in.
In the key of C, C is I (they use Roman numerals for some reason), F is IV and G is V.
And the exceptions also follow a pattern.
Practice: Write down the I, IV and V chords in the keys you commonly use. Don't use the chart.