the air coming out the vent should be chilly.
if not something is wrong.
did the a/c work before you hooked up the new thermostat?
if so that is likely the problem, usually you have your hot wire, and then 3 other wires (a/c, heat, fan. if I remember corectly mine was black for main wire, blue for a/c, red for heat, and white or green for fan). could you have hooked the wires up incorectly so that when the a/c is selected it just turns on the main blower. also if you went by color-coding and did your part corectly it is possable the wires are wrong at the main control unit(usually a schematic on the inside of the access panal). on the heater usually.
you can do an easy check by hooking the other wires up to the power wire one at a time and see which is which. one should run heat, one fan, and one a/c. let them go for a bit until you are sure which system is running and label each wire. then hook them back to the thermostat. if the a/c works when wired like this and you had the wires hooked up corectly then you may have just bought a POS thermostat
if you are sure the thermostat is ok and hooked up corectly and you still get no cold air out of the vent then I wouldn't recomend doing anything else yourself, you'd not likely be able to fix most problems and if you screw it up worse you may end up taking the problem off your landlords hands by making it your fault