The most basic style of playing guitar is strumming. You just need to make the chord shapes with your left hand on the fingerboard, pressing the strings down firmly and changing chords smoothly, then strum the strings near the sound hole with your right hand.
Listen to the song that you want to play (a recording, performance or just your own version- to "hear" the rhythm clearly.
To start with, just strum down with your thumb, from the thickest string (actually the lowest in pitch) to the thinnest string. Do one strum for each beat. Try to make the first beat in each bar a bit stronger (e.g. ONE,2,3,4, ONE,2,3,4, etc, or ONE,2,3, ONE, 2,3 etc if the song has a 3/4 waltz rhythm ).
If you would like to watch a video clip of this simple strum, I have made a couple of short clips (very basic- horrible singing, sorry). They are:
Mockingbird- http://www.youtube.com/watch?v=0OH81RpPJxQ and
Tom Dooley- http://www.youtube.com/watch?v=czIUFFuPmTc
Practise until your down beat becomes smooth. Then you can try a little flick upwards between each downward strum, so that you can get a bit of rhythm going.
Once you are more confident, you can vary the pressure a bit more to mark the beat (DOWN up, DOWN up, if it's a song in regular 4/4 timing, or DOWN, down-up, down-up for a 3/4 song such as The Streets of Laredo.
Then you can try using your fingernails as well- perhaps just your thumb and first fingernail at first. Work out what's most comfortable. If you curl your fingers up so your first 2 fingers are lightly touching your thumb, with your wrist nice and loose, you can flick up and down smoothly, catching the strings on the up- and down-strokes.
If you really want to use a pick, you'll need to work out how tightly to hold it, and the best angle to use. If your guitar doesn't have a scratch-plate, I wouldn't recommend a pick. It's easier to pluck the strings with your fingers, too.