Put car in gear (if you have wheel with gear lever, depress clutch, move gear lever into first), then press the accelerator while lifting clutch - same as you would do in real car. If using keys or mouse, check which key is bound to changing up a gear, and press that, then press accelerator key.
If the car will only go to certain speed, change to 2nd, 3rd, etc. If car doesn't go any faster after changing gear, then make sure the speed limiter (L key) isn't toggled on. If on, pressing L will toggle it off, and if off, L will toggle it on.