Listen to a lot of rockabilly. Notice how the guitarists are playing chords, and finger-picking or picking the notes out so that the high notes are on certain beats. Pay attention to the upright bass. The bass is played by slapping the strings while holding a note, and usually the bass line moves up and down the scales in a melodic country fashion. The drummers play simple beats. The Resources section below lists several bands you can listen to.
Learn to play the song you want to change as it is. For example, if you are learning a rhythm and blues song, learn to play it the way it was written. You can use sheet music to learn the chords and notes, or if you play by ear, you can pick out the song.
Change the beat of the song you're changing first. Rockabilly is upbeat and plays fast. Swing-dancers love it. The drummer should pick up the pace and play it with a little bit of a swing rhythm.
Change the bass. The bass line should dance up and down the scales that mirror the chords. For example, if you are changing a country boogie song in the key of E Major, play the bass line in that key moving up and down the bass. Learn to play slap bass if you don't already know it. It takes time and practice to get it down, but it will produce a dancing, swinging sound while slapping to the beat of the drums.
Change the guitar. You want the guitar chords to be picked rather than strummed. Think of Elvis Presley songs or some of the songs you listened to in Step 1. Try playing the chords of the song you want to change by picking out the chords in a catchy, flashy way. For example, if you are changing a blues song in E Major, you would play the chords picked in that key with emphasis on high notes played in appropriate places with the bass. Experiment and make the songs your own in rockabilly fashion.