Some good advice above, plus you may want to read the "Cakewalk 10 Microphone Placement Techniques for Acoustic Guitar" article, which is good. I can't seem to post a link here, but you can easily find it online.
There are lots of positions you can try out, and you have to experiment. You will probably also need to play a bit with EQ to get the sound you want. The room is very important, as people have noted. Try recording in different spaces or moving stuff around in your room to change the sound of the room, or even recording in different areas in the room to deaden or liven up the sound.
As noted, if you're just doing guitar and vocals, it can really help to widen the guitar and place the vocal dead center, either by hard panning two mic's, or if you are just using one mic, using some other technique (like just making a copy of the track in your DAW, delaying it almost imperceptibly and then panning the two tracks R/L). Otherwise, as you say, they can be fighting for space. Leaving them mono and putting your guitar slightly off center and vocal slightly off center in the other direction doesn't sound that great in my experience.