Some people would say you need to use a minor key for a melancholy feel- I disagree because Adele's 'Someone Like You' is major and feels very melancholy.
Different chord progressions feel melancholy in different contexts. There's not much advice I can give you because sad chord progressions are very diverse- there aren't really any dos or don'ts. Learn basic major minor triads and inversions then just mess around a lot.
You could use hooktheory or similar if you don't have access to a keyboard, but it's only a beginners tool really.
