Look for a key signature. If there is a key signature, then all you have left to do is determine whether the progression is in major or minor. If you do not know how to identify a key signature, simply count the number of flats or sharps and then use a circle of fifths table to identify the two possible keys.
Identify the quality of the first chord. If the first chord in the progression is major, then the key signature is a major key signature. If the chord is minor, then the progression is in minor. Minor chords consist of a minor third between the root and the 3rd, and major chords have a major 3rd between the root and third.
Analyze the rest of the chords in the progression. If there are several accidentals other than the 7th of the scale degree in minor, then you are dealing with a chord modulation or a chord succession. If either of these is the case, then you can only determine the key of the start of the progression.