Learn a few basic piano chords by doing research on chord techniques in books and online. You may already know some. If not, you can purchase a book of piano chords in a music store. You can also find piano chord dictionaries online, free of charge (see resources). It isn't necessary to learn to read piano music melodies unless you want to play more complex versions of love songs. For starters, playing the chord shapes while you sing the lyrics will be a good start.
Find sheet music to one of your favorite love songs. You can find sheet music to most popular love songs at any sheet music or instrument store. Study the sheet and use your chord dictionary to learn the chords in the song. Once you have learned the chords, begin practicing the song slowly. Just worry about playing the chords and singing over the top of them. Listen to a recording of the song if you can, just to help you hear the timing. The key during this run is to feel the chord changes and practice singing the words on cue.
Add a melody line and little fills as you progress and are able to play the chords and sing up to tempo. Since your vocals will be covering most of the melody line, you will want to tasteful add bits of the piano playing the same notes as your singing, more to enhance your voice than to match it note for note. Playing the melody line while you sing it can make the song song cheesy. Let the chords and your voice do most of the work. Use single notes inside your chord shapes to lead you to the next chord or to fill in gaps when you aren't singing.