Bob is right... a 24 gear bike won't let you go any faster... but to answer your question...
You'll need
1) an 8 speed cassette or freewheel (if you have a freewheel know that they are notoriously hard to find),
2) an 8 speed shifter,
3) an 8/9 speed chain,
and possibly new chainrings (if the chainrings are 6/7 speed), a new rear derailleur, and if the bike is entry level ,possibly a new front derailleur as well. If the rear wheel can't accept an 8 speed unit then you'll need a new rear wheel as well. It might also be necessary to reset the frame for wider spacing. If this is the case and you have an aluminum or carbon fiber frame, forget it.