There are many different performance situations where you would want to amplify your hammered dulcimer. If you are doing more than just jamming with friends, playing at home, or playing for more than a few people, then sound reinforcement is almost necessary. There are several ways to do it.
Cheapest and easiest is to just point a standard dynamic mic like a Shure SM 57 or SM 58 at the dulcimer from above, and hook it to whatever sound system is available. These work well in most situations, but if sound volumes are high, they can start to feed back. Also, they aren't very sensitive, so the closer they are to the dulcimer the better, and sometimes they can get in the way. The closer they are, the less they pick the other sounds going on in the room, so there's a happy spot somewhere above the treble bridge, coming in from the top, and just high enough to be out of the way. If you have two of these mics, you can do a better job of picking up what you are doing pointing them at the dulcimer from either side. The dynamic mics don't pick up everything that your dulcimer does, but are a pretty good choice for live performance with a band. Sound techs usually understand them, and can get your sound to come through farily well. Sometimes you can point a dynamic mic at the back of your dulcimer and get good sound, especially if there is a sound hole there, plus the mic will be out of the way, so it can be really close to the dulcimer which will exclude sound coming from other sources. You might tell the sound tech to cut the highs back, and try boosting the midrange and possibly basss on your dulcimer.
There are several different onboard pickup systems that can be built in to your dulcimer, or installed after the fact. They are all piezo type pickups which is the same thing installed in the street which senses your car is there when you stop at a light. The pickups are small and light and can be adhered to many different points on your dulcimer. Some folks just buy the piezo elements which are very cheap, and glue them to the under side of their soundboard in several different location, then wire them to a jack. Drawbacks to these systems are they will need some type of active (battery powered) control box to run through before sending the signal on to the sound system. The control boxes are readily available, since this is guitar technology, but can be quite expensive. Then there is hammer noise to contend with which these systems will pick up strongly. If the pick up elements are on the sound board, hammer noise can be very bad, and distracting. They are also prone to feedback with the pick ups installed on the sound board. This can be lessened by putting them on the rails or pin blocks of the dulcimer, but this also lessens how sensitive they are, so you have to turn the control box and possibly the sound board way up. You'll never get rid of hammer noise completely with these systems.
There are a couple professional systems made for hammered dulcimer that work. Schatten makes a two element system with the pick ups embedded in a silicone block to lessen the noise, and they sort of work. They also sell a control box to go with the system, but it is pricey.
Another company called Pick Up The World makes a nice system which is complete based on two ribbon pick ups which I have found best to install one on the lower rail, and the other on the upper rail. There is also a control box, and the system works quite well. Their system is meant for retro fitting to the outside of the dulcimer, but then there are wires running everywhere, and things to get banged up. It could be installed inside, but that would be best done while the dulcimer is under construction. Then there's the cost, some where north of $500.00. But if properly installed, it works pretty well, sounds surprisingly warm, and is quite feedback resistant.
So since I don't like the piezo systems, I stick with microphones, and have found what I believe to be the Holy Grail of hammered dulcimer mics. The Audio Technica 2035 is a studio quality condenser mic at a very affordable price. Condenser mics are more sensitive than dynamic mics, and the AT 2035 hears everything your dulcimer is producing very clearly. Since there is more and better information being sent to the sound board, it can be adjusted, and you can get the sound you want out of the speakers. Condenser mics need power fed to them from the sound system, it is called 48 volt phantom power. Most sound systems have this capability, but free standing smaller amps do not, so small, cheap battery powered boxes are available to put in line between the mic and the amp to make the power. You can sometimes pick them up for $20.00. The AT 2035 new price is around $150.00, and will include the shock mount holder to put on the mic stand, and a bag for the mic. The mic has a 10db pad switch, and a low cut switch, both of which I use when recording with mine. The only drawback I can think of with this mic is it could be feedback sensitive in high sound volume situations, like a loud praise team at church. For general use, though, I think it is the best. When recording, two of these mics would be good, one on either side of the dulcimer from above. They would be out of the way, and the sound will be very clear. But then, of course, we are forced to be really good with our playing!
My friend Rick Thum told me about another mic which he uses, and it is good. It is called DPA d:vote 4099G. DPA stands for Danish Professional Audio. The mic is very small, and used for all different sorts of instruments. The G at the end stands for guitar, and indicates the type of holder they include with the mic system. You attach the mic to the cool little holder, then attach that to the edge of your dulcimer and point the mic, which is directional, across the sound board. It requires phantom sound, and is amazingly expensive, full retail is $600+. The mic is really hot and faithfully picks up every nuance of what the dulcimer produces. It doesn't color the sound at all, very transparent. If you are prepared for that, it is wonderful. Great for solo performance, and in a small group onstage. I used one in church, and it was picking up the neighbors on either side, too until the sound guy figured out how to set it. Then it worked well.
For recording videos in my little office, I have found the best setup is just two Shure SM58s. Since the room is small and not well sound proofed, both the AT2035 and the DPA mic will pick up too much room noise and echo. So the video setup is a Canon EOS Rebel T2i SLR camera which I bought for still photographs, but will also record video in full HD. But the camera has an automatic gain control which is annoying. If there isn't sound coming in, the AGC turns up the gain trying to pick up stuff, then turns it back down when something comes in. It makes a rumble on the video. So to take care of that, I have a Beachtek DXA SLR interface. It will accept two mics, and record in stereo, but uses one channel to make a low hum which is below the threshold of hearing, but which the camera hears, and sets its gain accordingly, so the level going into the camera is uniform. It works great. I can plug two mics into the Beachtek but have found that it only records one side that way when set to kill the AGC, so I also have a little Mackie 1202 VLZ3 mixer. Plug the two mics into that, then two outputs into the Beachtex, then into the camera, and I have stereo. The mixer has tone controls, and also pan knobs, so I can set one mic to go into one side of the stereo, and the other into the other side. I only need a little bass boost, and usually set the treble and mid at unity since I am trying to get the most accurate recorded representation of the actual sound I hear acoustically. I also have a decent pair of headphones so I can hear exactly what is going into the camera as I am recording.