Practice
The more frequently you can practice the faster you will see progress in your playing. People can be born with a great voice, but no one is born with any natural talent to play an instrument. Learning to play an instrument is only a matter of practice. The more often you practice, the better you will get. This becomes a positive feedback loop - the more you practice the better you will play and the better you play will make you want to practice even more!
Remember - All practice will result in progress even if you can only practice once a month! You will progress faster the more frequently you can practice.
Aiming for 10 - 15 minutes a day and building from there is a great way to start!
Please don't start with long marathon sessions of practice because you won't be able to keep doing those!
Practice with a purpose on a Mt Dulcimer:
Find a quite place to play where, hopefully, you won't be distracted
Try to practice in a quiet space where you can clearly hear how you are playing. That means don't have the TV, music, or the latest podcast on in the background.
If you need to listen to a song to hear how it goes, listen to just that song and then set the device down!
Before you begin stretch fingers, hands, neck, shoulders, and back
The first song you should play is one you like and that you play reasonably well
Spend a few minutes each practice session working on left and right hand coordination.
While strumming or picking with one hand, play random notes/chords with your fretting hand (this is specifically not practicing a song) Try to watch both your hands at the same time while you do this. Remember, for smooth playing, your transition from one note or chord to the next with your fretting hand has to be fast but your strumming/picking hand has to stay with the same rhythm. Essentially, with your fretting hand you want to hold the note or chord for as long as you need to until quickly moving to the next note or chord and at the same time with your strumming/picking hand you want to keep a steady beat. (At first, it isn't easy to do two very different things with your hands at the same time!)
If some aspect of your playing isn't quite working for you, practice that aspect specifically for a few minutes.
If your strumming isn't as steady as you like it, just strum the open strings for a few minutes.
You can also practice strumming when away from the dulcimer by strumming against your leg whenever you hear music with a strong beat.
If your fretting hand seems to be getting tangled up, just fret random notes using different fingerings.
You can practice fretting when away from the dulcimer by pressing the fingers of your fretting hand down on a table pretending to follow the tune as you hum it or let it play in your head.
Then when you practice songs ...
Before you play the tune, sing/hum it either out loud or in your head. This cements the tune in your brain and helps when you try to get the tune to come out your fingers on the dulcimer!
Play as slowly as you need to.
Play only the melody if you need to.
To learn troublesome transitions ...
First try different fingerings to see what is going to work best for your fingers on your dulcimer
Then play just that little section that is hard, even if it's only a few notes, over and over again as slow as you need to make the transition. (It can drive my husband nuts when I do this!)
Once you've played that tiny section many times, back up a measure in the music and play through the troublesome transition a few times again starting the measure before. Only then go back to the beginning of the song and try the whole song again. If you flub that section still, don't worry, just keep doing this each time you practice the song. I promise that eventually you'll play it smooth and then wonder why it was so hard to begin with!
After practicing songs or in between different songs, spend some time just "noodling" around. Play random notes and transitions and see what sounds good to you and what doesn't. (You just want to experience the joy of the musical sound without worrying if you are playing a particular song correctly. )
End each practice session with a song you like and that you play reasonably well (it's fine if' it's the same song you began with!)
Then lastly - take a minute or two and savor the joy of that playing your dulcimer brings you.
Some people like to record all their practice sessions. If you can do that without getting distracted by other things on your device it can be helpful. But - you probably don't want to listen to those recordings right away. Instead record them over 4 - 5 sessions of playing the same tune, then, not during your practice time, listen to the progress you made between the first recording and the last one. However - be honest with yourself! ... How much time are you spending of your precious practice time just fiddling with your phone trying to get it to record. Or how much are your criticizing yourself and your playing when you listen to the recordings! If you are playing with your device too much or criticizing yourself too much, recording your practice sessions will be counter-productive to making progress.
Things NOT to do while practicing:
Don't worry if you think you aren't making progress. Just keep practicing. You won't notice the progress until you can look back after a long while (months at least) of consistent practicing.
Don't criticize yourself! Learning to play an instrument is very frustrating and de-motivating. You have to power your way through that. If thoughts like "I'll never get this" come into your head push them aside and just keep practicing. Seriously, you are getting better even if it is so slowly you can't tell from one day to the next.
If you don't already sight read musical notation (the music staff with notes) don't try to learn that while practicing your dulcimer!
This may seem counter-intuitive but ... please believe me ... trying to read the music while also learning a tune is a distraction!
Reading the notes won't help you learn to play them on the dulcimer. Instead focus on the melody of the song and try to play the song not the notes. You can do this by singing or humming the song, either out loud or under your breath, while playing the numbered tab.
If you don't know how a song goes you won't be able to figure that out from the musical notation unless you are able to sight read music already. Instead, find the song in youtube and listen to it over and over again until the song is in your head.
If you want to learn to sight read music, do that separately from your dulcimer playing practice. There are many, many books and resources online to help you with this.