one easy way is to count the sharps or flats that are repetitive in the chords. if there are 2 #s yer in D. one flat is F. ya know the circles of sharps n flats ? sometimes the chords kindo step outside o the normal theory structure so ya can , if ya see 2 major chords a step apart, hope to assume that the higher one is the fifth of the key ( if ya see a C and a D assume its in G )i always try to see it as in the key with the fewest incidentals.
ya know ? them notes that ya only strike in passing on occasion but are not 'in' the key ?:)