Here are a few general tips:
Expand the bassline (e.g., descending whole steps, moving around the circle of fourths, etc.), then harmonize the added bass notes with chords that fit the melody. For example, in m. 1 of Möge, the bass moves from an F to a C. So let's add stepwise chordal movement: F-Eb-Db-C. Now we have to find chords that work with the melody....
/ Fmaj7 E♭o Gm7 C7♭9 / Dm7 G9 Am7 D9 /
B♭ - F - / G Gm7 C7 C+ /
Fmaj7 E♭o Gm7 C7♭9 / Dm7 G9 Am7 D9 /
B♭ -C7 - / Fsus4 - F A7 /
Dm - A7 - / Dm - B♭6 - / Fmaj7 - G9 - / Gm7 Gm7♭5 C7 C+ /
The rest is up to you!
Ideas behind it are melody notes that are included in the chords, with some ii-V-I sequences. Use of ...