There are a few ways to find out when is it time for you to replace your car's tires. Inspect the tires properly, if the tread has worn down to about 1/16 of an inch. Some tires have a built in tread wear indicators. These indicators are designed to let you know how wore out the tires are, so you know when to replace them. Other tires have "wear bars", built for almost the same purpose. They are fixed in the tire and when the tread reaches the level of the wear bar, you will know its time to replace your tires. Another instrument a Lincoln penny is useful to determine the time to replace tires. It is like a meter that you just place facing your tire and check if the treads have worn out. If the tires just appear to be "bald", you will automatically know while driving the car, as it looses control during applying brakes or turning, but I suggest do not wait until its too late.
He's right go by the wear bars!
Black Circle tyre testWhile officially 2/32nd's is when a tire is worn out. I would suggest you watch this video on youtube that does a wet breaking test using a new tire, a tire with 4/32nd's, and then 2/32nd's. Safety First!