The biggest and possibly most expensive sign you need to change your engine coolant is your car’s engine overheats. Overheating is usually a sign that something minor was left to get worse. Know the color of your coolant when it is new. The three main colors are light green/yellow, orange and black. Check your coolant for proper level and color at least once a week. When rust starts appearing in the coolant, you’ll want to change the engine coolant soon. Rust, which shows up as a reddening of the coolant, clogs the cooling system, stifling coolant flow. This will eventually cause your engine to overheat.
For more info, see DIY Car Maintenance Servic: What to Do Yourself