This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
From: Douglas Gurr <firstname.lastname@example.org>
A request comes in for tyre mounting tricks. I suspect that this ought to be
part of the FAQ list. However in lieu of this, I offer the way it was taught
to me. Apologies to those for whom this is old hat, and also for the paucity
of my verbal explanations. Pictures would help but, as always, the best bet
is to find someone to show you.
First of all, the easy bit:
1) Remove the outer tyre bead from the rim. Leave the inner bead.
Handy hint. If after placing the first tyre lever you
are unable to fit another in because the tension in the bead is too great
then relax the first, slip the second in and use both together.
2) Pull out the tube finishing at the valve.
3) Inspect the tube, find the puncture and repair it.
Now an important bit:
4) Check tyre for thorns, bits of glass etc - especially at the point where
the hole in the tube was found.
and now a clever bit:
5) Inflate the tube a _minimal_ amount, i.e. just sufficient for it to
hold its shape. Too much inflation and it won't fit inside the tyre.
Too little (including none at all) and you are likely to pinch it.
More important bits:
6) Fit the tube back inside the tyre. Many people like to cover the tube in
copious quantities of talcum powder first. This helps to lubricate
the tyre/tube interface as is of particular importance in high pressure
7) Seat the tyre and tube over the centre of the rim.
8) Begin replacing the outer bead by hand. Start about 90 degrees away from
the valve and work towards it. After you have safely passed the valve,
shove it into the tyre (away from the rim) to ensure that you have
not trapped the tube around the valve beneath the tyre wall.
Finally the _really_ clever bit:
9) When you reach the point at which you can no longer proceed by hand,
slightly _deflate_ the tube and try again. Repeat this process until
either the tyre is completely on (in which case congratulations)
or the tube is completely deflated. In the latter case, you will have
to resort to using tyre levers and your mileage may vary. Take care.
and the last important check:
10) Go round the entire wheel, pinching the tyre in with your fingers
to check that there is no tube trapped beneath the rim. If you
have trapped the tube, deduct ten marks and go back to step one.
11) Replace wheel and reinflate.