3 strings vs 4 strings
Many dulcimers are sold with 4 strings. These are almost always set up with two strings close together as a "unison" (a.k.a "Doubled") melody string (see the picture on the left below). Meaning that those two melody strings should be tuned exactly the same. And there in lies the difficulty!
It is often very difficult to get those two strings tuned exactly the same. Then even if you can tune them the same, for beginners without tough finger calluses, it is very difficult to cleanly fret two strings at the same time. This will often lead to a less then pleasing sound. Many dulcimer instructors will suggest that you, at least temporarily, remove one of the doubled melody strings.
A very small percentage of dulcimers are set up with 4 equidistant stings (see the right hand picture below). There are some beautiful arrangements for this set up but it's an advanced way to play so it's not recommended for beginners.
PLEASE: Wear some sort of eye protection when you first bring a new string up to tune! If there is a problem with the string it will snap and you don't want any part of your eye in the way!
If your strings are very old, they can't stay in tune! Or they may not sound clear. The melody string on some dulcimers gives a twangy sound instead of a nice clear, bright tone when it's been more than a couple of months since the strings were changed. Strings age not just from playing but also from simply being under tension in the air. While you can wipe your strings off after each time you play to help, they will, eventually, get too old to play.
Ask the builder of your dulcimer for the proper size and type (ball end, loop end, wound, plain) of string for your dulcimer. They can likely sell you a set of strings as well!
If you don't know the builder of your dulcimer, here is a website you can use to approximate the size of the strings to use:
Here is a great short video on how to change stings on a dulcimer:
(They do use a doubled/unison melody in this video but you can ignore that second melody string if you want to)
For another good video that is a bit longer but provides a whole lot of more information about strings and other things is:
If you have violin-like pegs you may want to review this video to help those stay in tune better: