Decide whether you want to teach yourself or use an instructor. Different people learn better using a teacher, but some may be more comfortable teaching themselves from a book. Whether you use an instructor or not, purchase a beginning bluegrass guitar method and a chord dictionary. You can also find some of this material online at no cost (see Resources).
Learn a couple of basic bluegrass chords. C, D, A, and G are good starter chords. There are many positions a chord can be played in on guitar, so start by learning the chords in the first position, around the first five or six frets of your guitar. Make learning a couple of new chords a week part of your practice regime. A good chord dictionary in your head will allow you to be ready to play with other musicians in an improvisational setting.
Practice cross picking. This is a typical bluegrass playing technique that will improve your playing skills and give your playing a bluegrass feel. Cross picking involves using a flat pick to pick a pattern that repeats itself throughout the song. The pattern typically uses three or more strings, often played within a chord. A good bluegrass method will detail this technique; practice will help you perfect it.
Play as much bluegrass guitar sheet music as you can at your current level. Whether you choose to learn to read standard notation or tablature, you can purchase bluegrass music for guitar and find it online at no charge (see Resources). The more you play, the better your skills will become.