At times it is necessary to be active with only a small amount of rest. While it is unhealthy to be sleep deprived for any length of time, one can get by for a short period of time with only short, intermittent periods of rest.

[edit] Steps

Prepare yourself. If you know you'll need to get by without sleep one night, get a full eight hours the night before.
Set multiple alarm clocks. Don't let yourself oversleep.
Get up as soon as your alarms go off. No lounging in bed.
Start by being active. Do jumping jacks, go for a run, but do something to get the adrenaline going.
Follow your morning routine, whatever you associate with waking up. Shower, brush your teeth, whatever makes you feel like you are WAKING UP.
Caffeine may help when used judiciously. Coffee and tea are good. Don't add sugar or drink caffeine drinks with sugar (i.e. soda, red bull, energy drinks) as they will cause a crash.

[edit] Tips

Get plenty of rest at the next available opportunity.

[edit] Warnings

Do not do this more than once a week. Sleep deprivation can have serious medical consequences.
Do not drive, operate machinery, or make important decisions while short on sleep. You will be a danger to yourself and those around you.
You cannot assess your own level of tiredness. Just as being intoxicated makes it impossible to assess your level of impairment, one cannot assess one's level of exhaustion.