Method - Step 1a: Closely related keys
In tonal music, there are five keys that a piece is most likely to modulate too because they are most closely related (i.e. they have the most notes in common).
In G major, as in the example below, these are the subdominant (C major) and the dominant (D) plus the relative minors of all three keys. Put another way, it is the subdominant and dominant of the tonic key and of its relative minor (E).
If two keys are adjacent on the diagram they are more closely related than if they are not. For example, G major and D major only differ by one note, whereas C and D differ by two (F# and C# as opposed to naturals). Modulations between adjacent keys therefore sound much more natural and smooth.
In a minor key, it is the same but the other way around. In other words, if you were in E minor to begin with the five most likely are subdominant and dominant of both E minor and its relative major (G).