One old method that still works is called a gap buffer. The basic idea is that you put the text into a buffer, but instead of putting it all in one block, you create a "gap" at the cursor, putting all the text before the cursor at the beginning of the buffer, and all the text after the cursor at the end of the buffer. Most insertions take place at the cursor, which you can do without moving anything (until or unless you overflow the buffer). When the user moves the cursor, you move the appropriate text from one side of the split to the other.
Given typical controls (cursor left, right, up, down, page up, page down), the largest move you typically deal with is a page at a time, which is typically easy to handle quite a bit faster than a keyboard repeats. It can, of course, slow down a bit if you have a truly huge file and a "goto line" command, or something on that order. If you're going to do a lot of that, there are undoubtedly better structures to use...
