Definitely get a chromatic tuner, not something called a guitar tuner or dulcimer tuner.  There are lots of affordable models in the $10-20 range, but some are better than others.  I agree with John that the Snark is one of the better ones in terms of accuracy and ease of use.  Because of their low profile, I personally use the D'Addario tuners.  One is a headstock tuner that can work on a flat head.  But on my scroll-head dulcimers I use the same D'Addario tuner that's for violins or violas.  I attach it across the fretboard just left of the nut, where a lot of people keep their capo.  If you look at any of my videos when I play the McCafferty dulcimer, you'll see it right there.

If you want to spend a little more, perhaps the most accurate clip-on tuner is the Peterson Robo-Clip.  It uses a simplified strobe display that is much easier to read than older strobe tuners.  I use that on my guitar.

I also have an app on my phone called G-Strings, which is free and very accurate.  The only downside is, like the handheld tuners, it won't work at a jam or whenever there is significant ambient noise.

--
Dusty T., Northern California
Site Moderator

As a musician, you have to keep one foot back in the past and one foot forward into the future.
-- Dizzy Gillespie

Because I make and play a variety of instruments, I prefer a  chromatic electronic tuner which shows me not just the Note but the Octave that that note is in. 

These  days there are several that fit that bill, but I still love my Seiko SAT501 handheld.

I highly recommend trying an app called "soundcorset" it is very straightforward to use for tuning, and most modern smartphones have significantly higher quality microphones than clip on or onboard tuners. 
The advantage of a clip on is that it doesn't pick up background noise, which is useful in loud places like group settings. As John said, a chromatic is definitely ideal. 
While I can understand the apprehension toward using an app, the key benefits are that it's free and that it's built into something you already carry. Personally, I keep losing my tuners around my apartment, because I have too many instruments that arent well organized, so it's nice to always know I have the phone app as a last ditch, if nothing else.
Nate

@john-petry I like the idea of a clip on. The hand held is cumbersome for someone like myself who can't walk and chew gum at the same time! I've  tried the cell phone app thing... no bueno and I didn't like it. I have a smart phone... I think your better off without. I like Phil Robertsons podcast with his sons and Phil manages quite well never having a cell! The Mrs and I think our next phones (we don't have a landline anymore) are going to be  old style flip phones. We'll  start using our laptops more for the internet etc.

Years ago, a decent chromatic tuner would run $35 and up. Korg comes to mind.  Now there are loads of clip on type, that all perform OK, but my overall favorite is the Snark ST-2 model. Sells for about $13 on Amazon, What I like is that it is fully chromatic, so you are not tied to "presets" for different instruments, it has a nice bright easy to see display, and best of all it has the ability to use vibration or its own internal mic. [vibration mode helps in a noisy environment, as it's picking up your instrument, not everybody else]. It helps that it is built a little stronger on body than most other clip ons, and the clip has a good spring and grip. 

Although I don't have one of those newfangled cellular telephones,[I don't even have an oldfangled one].....I think you could probably find an "app" tuner if you looked.

I've never been able to tune by ear, so I'm looking for tuner recommendations. I've only ever had/used a Fender tuner, a small handheld type and I gave it away. I see there are tuners that call themselves "Dulcimer Tuners," in addition to guitar tuners. Thoughts?