Tyre fitting:
Check tyre for directional indicator, make sure you put it on the wheel the right way around!
Put first tyre bead in the centre of the 'well' on one side and rest that on the ground so that the weight of the wheel keeps the tyre bead in the well. Pull the rest of that side of the bead over the rim.
Part inflate the inner tube (check the repair is still holding) and with the valve-hole uppermost, place the side of the tube opposite the valve, into the tyre (this ensures that you don't pick up more dirt and cause another puncture). Ease the inner tube around and place the valve through its hole. Check the valve is square (ease the tube around gently if necessary).
Starting at the opposite side to the valve place the second bead into the 'well'. With the valve away from you, ease the sidewall in, pushing the bead into the well as you go. Once it starts to get stiff to push the bead over, place the valve-side of the tyre on the ground and starting again from the opposite side push the bead deeply as possible into the well.
At this point it is sometimes necessary (depending on the tyre cross-section)to deflate the inner tube again.
Continue pushing the sidewall in, from opposite the valve towards the valve; each time getting a little more of the bead over the rim. Be sure to push on the sidewall and not on the tyre tread (especially with studded tyres!), lifting the wheel with your fingers slightly. Working this way and aiming to get all of the bead into the centre of the well below the tube, will eventually result in the bead pushing over the rim without levers* to pinch it. It also means that the tube is pushed repeatedly up and away from the lip and bead, avoiding pinch punctures on inflation.
Inflate tyre to over-pressure (not too much!) and bounce it on the ground a few times#. This will help seat the bead and so centre the wheel in the tyre. Deflate to required pressure before riding.
*Tyre levers are often necessary to remove the first few inches of bead after breaking it away from the rim when removing the tyre, because you can't get your fingers in there to pull.
#Omit this step if in a hurry at roadside repair, but ensure the bead is seated correctly before any long ride.