Magic Stringing (Old)
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For now, a simple diagram of the stringing based on Jaap's magic page:

Now, how about something more explicit:

Infinitely accurate Extended Metafile
Lay out the tiles in order, rotating the bottom half of the magic around to the right of the top. Depending on the magic type and orientation, you might have to swap an end tile to the other end. You should begin with any odd tile of this cyclic ordering (1st, 3rd, 5th... but not 2nd); if you don't, the Magic may not fold into the correct pattern. The regular Magic should begin in the upper left-hand tile, the Master Magic requires shifting for the common orientation.
Note that to string between tiles already in place, you can simply pull the string through the small gap to the string crossing junction; all added strings go onto the outside of anything in place.

1. Take the first three tiles, and perform stringing A, You can twist the last tile to put the string into place without strectching.
2. Flip the Magic vertically, and do stringing B on the back. With a small lever (a thin, long bar slightly bent in the center would work best, but a paperclip works if you're carful), this should require little force. The tiles should already be attached firmly enough; in fact, they are theoretically enough to hold the magic together. If you are running a bit low on strings, do the first two stringings for each, and one of the next two (I use #3).
3. Flip the magic back; do stringing B.
4. Finally, flip again and perform stringing A. There should be one of each stringing begun on both sides, in different orders.

5. Now, flip back to the original orientation, and add two tiles to the right. Repeat 1-4, using the three right-most tiles, until you only have one tile left to place.
6. Fold the magic into a ring, and carefully join the ends, with the last tile between them, with operations 1-4. You might have to do somthing creative to provide a workable area for the last few leverings. Ideally, you should try to string the thread under the first three tiles'. However, in practice, it's not that harmful, and since magics break, it's better not to have a loop. If you have to replace strings, you will probably have to undo at least the rest of the mgaic, until the the end of you stringing. If you place the last set correctly, you can avoid strings breaking there from the double-overlap, and "catch" the undo chain from the most likely breaking place (most often the lower right).
7. Fold the ring back into a rectangle, and begin having fun :-)