For me, learning guitar as a kid was a fun, natural, and very gradual process. But the thing that really grabbed me was Travis picking. I had learned to change chords and strum and sing along folk songs with other people, and occasional bass runs and arpeggios, but when my teacher came in with this Travis tune that was it! How cool was it to keep a bass going and play the melody at the same time! But it wasn't until I was an adult many years later that I actually heard the music of Merle Travis after whom the style was named, and I realized that what he was doing was really quite different from the Travis picking I learned as a kid. So, what I'd like to do is give you an intro to Travis-style picking and also work in some of those cool little details, some of the things that he was doing to give it that Muhlenberg County authentic sound.
Muting the bass — what Travis called "choking the strings".
Lightly lay the side of your palm across the bottom strings (usually the bottom 3, occasionally the 4th as well) so they sound muffled while the melody notes ring free. Experiment with where you place your hand to get just the right amount of muffle. Too close to the sound hole and the strings will be completely muted, too close to the bridge and they'll ring out too much. Find that spot where you like the sound and you're getting just the amount of muffle you need.
Thumbpick
The thumbpick gives more volume and attack to your bass notes and its traditional to use one in this style. Make sure you get one that fits your thumb snugly, so it won't move around while you're playing. I sand mine with several grades of fine sandpaper or cloth nail file just like I would my fingernails to get a smooth edge.
You can also play with your bare thumb. Because of your hand position, you'll be using the side corner of your thumb instead of the nail.
Lightly Bracing the Pinky on the Face of the Guitar
Normally I don't recommend this because it makes your hand tense. I started out bracing my pinky and it took me a while to "unlearn" it, so I could have a nice relaxed feel over the sound hole. But when you're playing with a muffled bass, your hand is in a position where it doesn't cramp up your hand, so if it helps you to have more stability, go for it!
Move the Thumb in Little Circles
This movement makes switching between the bass notes smooth and helps you to keep the all-important beat.
On Beats 2 & 4, Hit More Than One String on the Bass
I first learned fingerpicking with all separate, clean bass notes, like Chet Atkins, but Travis just made a swipe to hit two or three strings at a time instead of just the 4th string in beats 2 and 4 to approximate the bass chord as played by the left hand of a stride piano player.
Bass Notes
I first learned to always play my bass notes starting on the roots of the chords and play an alternating bass, but much of the time Travis just kept playing the 6th string. Also, instead of the root (1) he also often played the 3rd or the 5th of the chord in the bass. This gives the music a unique sound.
Use of the Thumb on the Neck to Fret Notes and Play Bass Runs
Travis fingered many of his bass notes with his left hand thumb around the back of the neck and even did bass runs with it. He had big hands and a skinny neck guitar. I have small hands with a fat neck guitar, so I don't do it as much, but if you can, go for it! I worked a long time on barre chords but with that thumb around the top, but Travis almost never made a full barre chord, he just used his thumb around the back of the neck.
Two Fingers are Enough
I learned to play using four fingers, with my right-hand thumb covering the bass notes and my index, middle, and ring covering strings 3, 2, and 1, but Travis played all his melodies with just his index finger. Either way is fine.
Syncopation
There's a lot of syncopation; playing the melody notes in between the bass notes, anticipating notes. That's really important to this style. I'll be giving you exercises to work on that.
Good Solid Beat
Last but not least, really lay into that beat. Some of these exercises may seem really easy and you'll want to play them fast. But it's harder to play it slowly and get that really solid feel going. It helps to play along with other people and just do that accompaniment for a while. Chet Atkins said half-jokingly that all he did for his first two years playing was go back and forth between two bass notes! Just do it for a while. Don't add any fancy stuff until you've got a good solid feel going.