Replacing tyres is quick, easy, and can massively improve the ride of your bike.
Remove the wheel(s) of the bike you intend to operate on. If it's a normal bike, this will done with just a 15mm spanner.
Some tyres are designed to work in one direction better than the other for improved grip/speed. Look at the sidewalls of your new tyre, and identify which way around it needs to be (if any). Place one bead on the rim.
The last section of the beading is often quite tight with new tyres, so you might need the levers again. (Be sure not to puncture the inner tube, again!)