How do you find a melody for a song?

I often find myself sitting with my lyrics unable to find a fitting melody. Then I listen to all kinds of amazing songs and wonder how it can be so hard. Some of the songs only has two or three chords, so they are very simple.
I have written a few, totally finished songs, but I often find it hard to find a fitting melody that captures the mood I want.

Any one you guys have any experience with songwriting? Do you “find” the melody on the piano or another instrument and then write it down in notes or do you just chose some chords and sing a melody?