If you just got this unit, sometimes the electric utility can tell you what the usage was like in past summers. You may have to go to their office or customer service center in person and ask, and maybe bring a copy of the deed or mortgage, to show that you own the property.
Assuming it's central air, go to the place and take a new filter with you. Install the new filter no matter what, but take a look at the old one, and inside the furnace, before you close it back up. Is it full of dust or pet hair or something? Maybe the filter needs to be changed more often. If the blower wheel is plugged up full of hair, get an HVAC tech out to clean it.
Go around the house to all of the air vents, and make sure the flaps in them are open (use the little handle/lever/knob that sticks out of the grille), and that they don't have a rug or furniture or something blocking them off.
Sometimes people will turn the thermostat down and then close the vents to try to regulate the temperature - if this goes on long enough, the evaporator (A-coil, inside coil) can get ice on it, which really blocks the air flow. Unfortunately the coil is inside the ductwork and hard to see without taking stuff apart, but if you see ice or frost on the outside of the coil, or on the copper Freon lines at the furnace, that may be what's happening. The fix is to open up the vents and set the thermostat to "fan only" for a few hours to melt the ice - this will cause water to drip around the furnace, so maybe have some towels or a shop-vac ready to clean it up.
If the outside unit has never been cleaned, sometimes it will cause the A/C to work harder. It can get plugged up with dirt, pollen, seeds (are there cottonwood trees around?), bugs, etc. The fix for that is usually shutting off the power at the box on the side of the house where the cable from the A/C connects, hosing it out with a garden hose (use a wide spray nozzle rather than a thin "laser beam" of water, so you don't bend up the fins on the condenser), letting it dry out for a couple of hours, and then turning the power back on. If you can, do this in the evening or on a cooler day, because the A/C will be off for a couple of hours while you do it.
If none of that helps, it might be time to get an HVAC tech out. He or she can see if you have a Freon leak, or if there is some other problem. Plan on at least $100 for the service call, plus any parts they have to replace.