The easiest way to find the relative minor of a key is to count down three semitones from that note. For example, for C major (no sharps, no flats) you would need to count down three semitones from C. This would lead us to A. Drawing a simple diagram of a piano can help you do this (or using the keys in real life).
The key signature for a relative minor will be the same, so when identifying a key signature be sure to look at the music to know if you are dealing with the major or minor in the first place. Clues include raised 7ths (for example the Gs in A minor will be sharps, indicating the minor key) and the tonic note (first note of the scale in that key).