Step1
First off, a domra is a lot like a mandolin. It has a bowl back, but the bowl is not elongated like the Italian mandolin in the movie “Captain Corelli's Mandolin”. Instead, the back of a domra is as round as if you'd taken a pumpkin and cut it in half vertically. In fact, there are some legends that the original domras a few hundred years ago were indeed made from gourds. So once you know what you are looking at, you can choose whether you want to learn the 3-stringed or the 4-stringed domra.
Step2
There is some mild good natured rivalry between players of 3-string domras and 4-string domras. If you live in a city where there is a balalaika and domra orchestra you are considering joining, you might find out what most players in that orchestra are playing before you invest your money. Some players can be serious about the 3-string vs 4-string rivalry, as the the 4-string is considered by some to be more Ukrainian than Russian. To be honest, though, in tone and sound quality, they sound exactly the same, because they have the same body shape. The 3-string just doesn't have quite the range in the lower notes that the 4-string has. But serious world master domra players have mastered their craft on both sides of the fence, so whichever you choose, you have some heavyweight opinions on your side.
Step3
You've chosen your instrument, and the first thing you need to do is tune it. Well, even though it's not a mandolin, a 4-stringed domra is tuned exactly the same as a mandolin – G D A E. But of course, it takes only half as long to tune it as a mandolin, because it has half as many strings, since the mandolin actually has 8 strings, tuned in pairs. The 3-stringed domra will be even quicker to tune - D A E. You can match the pitches to a piano or accordion, or use one of those modern electronic tuners that are so common these days.
If you have the 4-string, you will notice that the G D A E tuning is also exactly the same as the tuning for a violin. If you come from a violin background, you are a natural for picking up the domra.
Step4
Holding the domra -- If you've never played a stringed instrument with a neck before, it will probably take you a week or two to get comfortable holding the back of the instrument against your body, particularly because this one is so round, with the strings facing away where you can't see them. Take your time. Soon enough it will become second nature, and your left hand will know just where to find its notes on the strings and frets. You might practice with some scales, or even take some lessons if you are entirely new to playing music. You can get there. Many people take up music in midlife or later.
Step5
Using the pick -- If you've played mandolin before, you will likely notice that the experienced domra players around you are not holding the pick the way a bluegrass or folk mandolin player often holds it. In fact, even the pick is not the same. The pick for the domra is about half the size of the usual pick you find in a guitar shop. Domra players don't play as many chord rhythms as mandolin players, and the music for it is a lot more orchestral and classically based. To make your domra jump with volume, you need a tight grip on your pick. Make a fist with your right hand, with your forefinger curled around to touch the base of your thumb, with your thumb resting against it. Slip that little pick in there, between the forefinger knuckle and the thumb. You are not going to play from the wrist, but you are going to play from the elbow, keeping the wrist nearly straight most of the time. Neither do domra players rest their right pinkies on the face of the instrument. You want that right hand to have the freedom to move without an anchor.
Step6
Have fun, take in some concerts, join a balalaika and domra group, and pretty soon, you'll be giving concerts too!
Novice 
