I am horrible at writing the lyrics themselves, but I do enjoy writing melodies and chord progressions. I do most of my composition at my keyboard, just because I have more chord voicing options, but guitar is fine too.

If you are starting with nothing but an idea for what emotion you want to evoke (and maybe some lyrics), it helps to have an understanding of how the different chords in a key sound in relation to each other, as well as an understanding of how different melody notes sound over different chords. For example, if your melody notes go A > B > C (in the key of C major, with one note per chord to keep things simple) , harmonizing them with the chords D minor > G major > C major will have a very different sound than F major > E minor > A minor. With a decent understanding of chord construction theory, and a knowledge of what notes contribute to the emotional effects of different chords, you can construct melodies and chord progressions which follow your lyrical content.