Answer for USA, Canada and countries running a 60 Hz supply service.
There is a device that you can pick up from a DIY store. Ask the clerk to show you their duplex breakers. The one that you should be looking for is a 15-30-30-15. This will allow you to remove two 15 amp existing breakers and install this new one. The two existing 15 amp circuit loads will be connected to the new 15 amp positions on the new breaker. Your required 30 amp load will be connected to the center position on the new breaker.
It depends on what you mean by the breaker panel being full. It depends on the equipment involved and would require more detailed information about the existing electrical panel.
If you don't know the answer, contact a licensed
Take two breakers out of the box and add a high power 240 volt circuit. Run that to a subpanel, and add the breakers (including the two you took out) to the subpanel.
Remember that the safety ground and the neutral must be kept completely separate in the subpanel.
As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.
Before you do any work yourself,
on electrical circuits, equipment or appliances,
always use a test meter to ensure the circuit is, in fact, de-energized
IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB
SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.