Another concept you should be familiar with when transposing is the Circle of Fifth Theory. This theory is a simple way to understand key signatures. By starting at any key, count seven keys to the right or left (both black and white keys) and you will find the perfect fifth. In other words, the perfect 5th is seven half steps, or the distance between the first and the eighth key.
If you start at C (which has zero flats and zero sharps in the key signature) and count upwards, G is the fifth key. G is the perfect fifth of C. The key signature of G only has one sharp. Then if you find the perfect fifth of G, you will find that D has two sharps. Then A, the perfect fifth of D, has three sharps and so fourth. Now, lets say you go back to C and find the perfect fifth of C counting downwards. You will find that F is the perfect fifth, and the key signature of F has only one flat.
Counting downwards again, you will find that the key signature of B flat has two flats. Continue on in this pattern for the rest of the keys. This theory will help you enormously in terms of transposition.
Being able to freely transpose songs to different keys is a talent that takes time to build. Stay positive and be patient. If you have knowledge of these concepts previously mentioned, you should have no problem transposing songs.
Here is a diagram of circle of fifth

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