For a front wheel: Hold the wheel on the ground, then pick up the bike and slot the fork onto the wheel. If the bike has disc brakes, be sure to slot the disc carefully into its caliper. Then, hold the quick release lever in one hand, and the opposite small nut in the other, and rotate the lever a few times, until you start to feel resistance. Then close the quick release lever in an upward or rearward direction, and feel it gripping firmly. It should take a little effort from two or three fingers to close it firmly. If the lever closes too easily, re-open it, wind in the nut on the other side of the bike a little more, then try again. If it’s too hard to close the quick release, open it, loosen the nut a little, then try again.
For a rear wheel: Hold the wheel on the ground, then lower the back of the bike onto the wheel. You’ll notice there are two lengths of chain in your way. Position the smallest gear sprocket beneath the uppermost of these two bits of chain. Let it slot into the chain as you guide the axle of the wheel into the dropouts. The lower part of the chain should remain at the bottom of all this, out of your way. On a disc-equipped bike, ensure the disc is lined up to slot into its caliper as you replace the wheel. This stage can be fiddly, so be patient, and don’t force anything. When the wheel is neatly back in place, close the quick release skewer. If the quick release lever closes too easily with too much difficulty, see the advice for front wheels above.
Give the wheel a spin to check all is OK. Test the brakes. You’re ready to ride!