An appliance designed for 240V absolutely must have a 240V outlet installed for it; there is no way to properly power it with 120V. If you aren't able to install a 240V outlet yourself, you should contact an electrician.
You'll have to install a double-pole breaker in your breaker box. As for the outlet, read the instructions and determine what size outlet (how many amps) you need. For the cables, if it's an air conditioner that requires 120/240V then you'll need a 4 conductor wire. (3 wires plus ground.) If it just requires 240V you'll need a 3 conductor wire. (2 wires plus ground.)
For wire sizes, some recommendations, which exceed the National Electrical Code, are:
15 Amps or less: 12 gauge; 20 Amps or less: 10 gauge; 30 Amps or less: 8 gauge;
40 Amps or less: 6 gauge; 50 Amps or less: 4 gauge.
Again, these values are over-sized but bear in mind that the actual length of the run is very important and must be taken into account when selecting the gauge of wiring to use for a new circuit. Best practice is to check with a licensed electrician or see Table 310.16 in the National Electrical Code.
If you do this work yourself, always turn off the power
at the breaker box/fuse panel BEFORE you attempt to do any work AND
always use an electrician's test meter having metal-tipped probes
(not a simple proximity voltage indicator)
to insure 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.
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