Accompanying yourself on guitar or backing up another singer requires the right approach and a certain set of skills. Your job is to play the kind of guitar part that supports the singer and the song and there are six things you can do to make that happen.
Keep it simple. In order for the singer to deliver a song in the most effective manner, the guitar can't be getting in the way. Start with a simple strum of basic chord shapes (this works as a great starting point) then go from there. A complex, busy guitar part can get in the way of the singing and ruin the song. Whether you are accompanying yourself or someone else, always keep in mind that your job is to support the singer, not wow the audience with fancy guitar licks.
Choose the proper technique for the style. Many songs sound best with a simple guitar strum while others really shine if you use a gentle finger picking pattern. Or you may find you need an electric cranked up a bit to give a song the needed energy and push. Make sure you discover the best way to create the perfect guitar background while staying true to the style.
Fill in around the vocal. In any song, there will be places where the vocalist takes a break, even between phrases. This is where you need to play a little something extra to keep the music interesting and entertaining. If you have an extended part of a song, such as an instrumental break, that's where you can stretch out a bit and play "more" guitar. It's best to keep the melody in mind and stay within the framework of the song.
Choose the best way to play each chord. There are a number of ways to play the same chord on guitar so it's a bit of challenge to play the right one (at the right time) for a particular song. For example, playing an Am chord in the first position might work best for a folk song but playing the same chord as a bar chord at the 5th fret might work best for Blues or Rock. Knowing a number of different chord shapes comes in handy.
Be consistent. First and foremost, keep the rhythm consistent. If there are trouble spots such as difficult chords in the song, practice them separately until you get them down so you don't interrupt the flow of the music. You may find you have to play certain chords in a simpler way to get the job done.
It's also important to be consistent in how you play including strumming the song the same way throughout or using the same finger picking pattern from start to finish. When backing a vocalist, keep your experimenting to a minimum.
Know how to use a capo. A capo allows you to change keys without having to play a whole new set of chords. Typically, if you play a song for a male vocalist, you can play the same song (and use the same chords) for a female voice by placing the capo on the 4th or 5th fret.
If you take the right approach and keep in mind that it's your job as a guitar player to help the singer sound great, you'll play like a pro in no time.