How do you change gears on an eighteen gear bike?

Isn't really clear what you mean by this, if you're asking for how to replace the gears or how to use them. Today 18 gears could mean either the you have 2 chainwheels (by the cranks) and 9 sprockets(at the rear) or that you have 3 chainwheels and 6 sprockets. These will yield 18 combinations, but not 18 usefully different gears. Expect to have maybe 12-14 usefully different ratiOS from 18 possible combinations.

How to use them:

An easy way is to basically use the front gears according to terrain, small front for steep climbs, mid front for average riding and big front for tailwinds and descents, and then use the rear gears to fine tune the ratio to where pedalling feels right. Also keep in mind that you want the chain to run as straight as possible, so you don't want to run it on both big chainwheel and the biggest sprocket simultaneously. Small-small is just as bad. As the ratiOS overlap you're not really missing anything if you do a shift at the front before you've run out of sprockets at the back.

How to actually shift:

there are a few versions of shifters available these days. It's the old-style basic levers, one for the front shifter and one for the rear. Twist the right one to change the rear and the left to change the front.

Then there's the gripshift where half the grip is a barrel-like thingy that can be rotated, just like the throttle of a motorbike.

Then there are the trigger shifters, with one lever/button for upshifts and another one for downshifts. just press and the chain will move.