If it was my fence, I would not want you repairing it, especially if you didn't know what you were doing. I have a particular way I like to do my splices, and I reckon so do most fence owners. Most people who don't know what they are doing want to tension the dickens out of a high-tensile fence, but for an electric fence, it is actually better to put the bare minimum of tension on as possible. The electric shock keeps the animal off the fence, and the slack in the line means that if a tree falls on it or something, the wire just stretches to the ground and doesn't break or pop the stand-offs off the fence posts. If my fence line broke, I would want to be able to inspect if any non-obvious damage was done, which I wouldn't get to do if somebody else repaired it without my knowledge. Finally, as others have pointed out, the fence may be hot, in which case it will need to be de-energized before working on it. I agree with what others have said: let the owner know about the break. He or she will have tools, equipment, and knowledge to effect the repair to his or her satisfaction.
To get to the answer of your question, the way to splice a high-tensile fence is to let some slack out of the strainer, splice the wire, then re-tension the line. There are two main ways of doing the splice. You can use a swage sleeve and crimp tool, where a double-necked sleeve goes over both wires, then a crimp tool crushes the sleeve against the wires. Typically, you will use three sleeves on an in-line splice and two sleeves when making a loop (e.g. around a fence post). The sleeves must be sized to the gauge of wire or they won't grip properly. Alternatively, you can make a "line-man's splice" knot. Here's a diagram:
The line-man's splice is very difficult to do on stiff wire like high-tensile. You can actually get small hand tools that help with twisting the wire neatly. If it is not done right, the wires will slip past each other and not hold.