Non-folding tyres are best folded into 3 loops. A simple figure of 8 can damage a wire bead.
Hold the tyre at 4 o'clock and 8 o'clock
Bring the hands together and grip both sides in one hand
Take 12 o'clock, and swing it away and down to the gripping hand to form 3 loops
Move the left and right loops together, swinging the bottom loop away and up.
fasten the 3 loops together at the top with a bit of string, a toestrap or whatever.
The same fold can be achieved in a number of different ways. If you can't work it out from the above, try looking on youtube.