AC units and thermostats have built-in delay features when they're shut down and then repowered. The delay can be as long as 10 minutes. And, if you've subscribed to an energy-saving device from your local power utility, the unit can take even longer to reset. If you've installed the parts shown and reinstalled the disconnect block, repowered the circuit breaker, turned on the switch at the furnace, moved the thermostat to AC mode and lowered the temperature below the indoor temperature, and the unit doesn't fire up after 30 minutes, it's time to call a pro.
You might also want to check your home for thermal insulation if you live in extreme heat or freezing temperatures. Insulation keeps the heat and cool air in your home, which can lead to a lower electric bill. If the heated or cool air leaks out, your system turns on more often. There are various types of insulation that you can install in your home and a home energy auditor can point out the best places for it in your house.
In addition to the information below, see these two articles for the general care and maintenance of your air conditioner: Preparing Your Air Conditioner for Summer and How to Replace Furnace & AC Filters. Most noteworthy, you should replace the filters at least twice a year, before the heating and cooling seasons. For information on furnace problems, please see Furnace Not Working.