There are a few things going on in a song, and with guitar you can participate in any or all of them. However, just starting out I think you'd do well to limit yourself to beat and melody.
The beat is the underlying structure of the song. All they rhythm takes place over the beat. Most rock songs have four beats that repeat over and over. 1 2 3 4. There may be a lot of rhythmic things happening in those four beats, but overall it's four beats. See if you can listen to something and get the underlying beat of the song. Just listening. When you can clap your hands or tap your feet constantly at the same speed without alteration and keep it going, you understand beat. Strum down once per beat. Sometimes you change chord on the 1 beat and sometimes on the three beat and sometimes on each beat. You have to listen for that. But first... listen for the beat. Often times Country songs - especially the genre now being called Alternate Country or Americana - is easiest to hear the beat.
Then the melody is what you may think of when you sing it. It rises and falls and is the recognizable tune that you would hum if someone said, "I don't know that song. Can you hum a little bit of it?"
If you can sing the melody while strumming down once per beat in time steadily over the song, you've met a significant hurdle for playing and singing. You'll neat rhythmic stuff with the strumming and learn to pick out a melody and enhance it over time. I've seen some guys in bars playing where they keep the beat with a bass line, play rhythm in the middle, and play melody as a lead lick all at the same time on guitar. It's extremely impressive, but that takes years of steady practice to get to that level. As a beginning, playing a steady, smooth strum without having to stop to change chords and being able to sing the melody at the same time is HUGE. As arkady said, it takes a great deal of practice. It also is not something you learn all at the same time. You have to learn the chords, smooth transition between chords, how music is constructed in beats and rhythm, how melody works, and in all likelihood you'll have to learn to sing too. You've got a lifetime of learning ahead of you, and no matter how much you learn and how good you get, there will still be more to learn. It's wonderful.
- Zurf
Granted B chord amnesty by King of the Mutants (Long live the king).
If it comes from the heart and you add a few beers... it'll be awesome! - Mekidsmom
When in doubt ... hats. - B.G. Dude