An air conditioner's manufacturing date can be found by looking at the nameplate, usually found on the back of smaller units or on the outside condenser of HVAC systems. If the manufacturing date is not printed on the nameplate, note the brand name, model and serial number for further research.
Building Intelligence Center carries a list of manufacturers on its website. Scroll down to the correct brand and find samples of nameplates and instructions for decoding the serial number. For example, if the manufacturer is Trane, scroll down to the nameplate that best matches the air conditioner in question.
Use the key to translate. Looking at serial number F91 - 90391, the code key notes that the F stands for June, and the 91 is the year. Some serial numbers are more complicated. Also looking at Trane, serial number 91531S41F breaks down as follows: 9 is the year, 15 is the fiscal year and 3 is the workday. This serial number gives a more precise manufacturing date.
Keep in mind that the manufacturing date may not be the installation date, but unless the machine has been stored, it should be close. The manufacturing date does determine the type of parts used and the maintenance requirements.