It's not enough that you have to keep your harp in tune and practice all the time, you also have to change any broken strings. All harps break strings from time to time, and any of the three materials used - nylon, gut and wire - can simply let go. This doesn't mean there's a problem with your harp, or the way that you're caring for it, but it's always best (both for the harp and your practicing) to put a new string on right away.
Many people find replacing a string a bit daunting the first few times they try it, but it gets easier. Part of what makes it tricky is that it's hard to get regular practice in. You might go six months without breaking a string, then break a few as the seasons change, and then have another few months off with no broken strings. Without a doubt, the best approach would be to change one string per week for a while until you feel really comfortable with the whole process, but no matter how nicely you ask, your harp is not going to obligingly break one string every Thursday, rotating through the different types, so that you can practice replacing strings regularly.
For a second best approach, I thought I'd put together a few videos that cover different aspects of changing strings. I hope they help!
How to Determine the Correct Replacement String. Before you can replace a string, you have to order a new string. Figuring out which string you need can be complicated, so this video starts with discussing the different materials of strings - nylon, gut and wire - and then goes on to talk about numbering systems to differentiate between individual strings.
Replacing a Gut String
This is a detailed approach of how to replace both a lower (thicker) gut string and a higher (thinner) gut string, including removing the old string, tying a knot in the new string, threading it through the harp, winding it around the tuning pin, tuning it, and clipping off the excess. Replacing a gut string is almost identical to replacing a nylon string. A pedal harp is used as an example. If you've never changed a string before, you can start here (or with the nylon string video).
Replacing a Nylon String
This video shows in detail how to replace both a lower (thicker) nylon string and a higher (thinner) nylon string, including removing the old string, tying a knot in the new string, threading it through the harp, winding it around the tuning pin, tuning it, and clipping off the excess. A lever harp is used as an example. If you've never changed a string before, this video is a good place to start.
Replacing a Wire String
This video explains in depth how to replace a wire string, including removing the old string, threading the new string through the harp, winding it around the top while leaving slack, tuning it, and clipping off the excess. Throughout the video the differences between changing a gut/nylon string versus a wire string are discussed. A pedal harp is used as an example. Most people first learn how to change nylon or gut strings and then work on their wire string changing skills.
Replacing a Full Set of Strings
Although harpists generally begin by just replacing strings as they break, eventually you may find yourself wanting to restring your entire harp. This video explains how to go about doing that and assumes that you already understand the basics of changing the different types of strings.