Determining how old your computer is may sound like a simple task, but there's actually a lot to consider. For one thing, your computer is made of various parts--any of which were possibly replaced at some point. So while various components that make up all your computer, such as your hard drive or RAM, may have a date on it, these don't necessarily reflect the age of your computer. In spite of this, there are a few fairly accurate ways to determine a computer's age.
Check the documentation that came with your computer, if you still have it. Simply check the dates included in the documentation, including copyright information and (if you're lucky) a manufacturing date. The most recent year you find is likely an accurate indicator of the year the computer was manufactured.
Find the manufacturing date in the BIOS.
The BIOS is a piece of software stored on a chip on your computer's motherboard. While operating systems are frequently reinstalled on a computer, this software is replaced less frequently, making its age a fairly accurate indicator of the age of the machine.
Seeing the BIOS is relatively simple, though how to do so varies from computer to computer. Turn your machine on and follow the on-screen instructions pertaining to entering the menu; typically this will be F2 though the actual key to press can vary from machine to machine. The BIOS is typically a text-based interface you can browse with the arrow keys--if the arrow keys are not usable there will be on-screen instructions. Browse all information until you find the manufacture date, or the date the BIOS was installed. This is a fairly accurate indication of how old your machine is.
Check the website of the company that made your computer.
Both the above methods will give you a fairly accurate indication of the age of your machine, but the best method is researching the date your model of computer was manufactured. Go to the website of the company that made your computer--examples include Dell, HP, and ASUS--and search for your make and model. If you don't know the model of your computer, it's likely written on the bottom of your machine (if it's a laptop) or on the side (if it's a desktop).
Search the company's website for your model and you'll find a variety of information about your computer--including the year it was made.