A simple thought here, but others have given you their best advice.

One of the happiest moments as a new songwriter is when you ask someone to perform your song... hmm... now how about do I go about this

well, to keep it simple

- join a guitar forum that the owner teaches its member to play their own music
- make some post to get known, but kind of don't push the songwriting wish out there just yet
- learn which members can sing and compose their own music
- after being on the forum listen to the " silent character " of the artist and see if one of your songs fits their personality
- make an into of yourself to that person by a PM
- have a song completed with your music and recorded ( the rawer it is, the better )
- ask a member if they'd be interested in recording the song for fun
- let that person have a 100% of their own creativity and take a back seat
- enjoy the ride with a smile

- the above is a 100% confidence builder for any new or experience songwriter

good luck

need a forum as such, PM me if interested