The only way I know of is to beg/borrow/buy a scanner/code reader and hook it up. It seems like Harbor Freight sells a bottom of the line OBD-2 code reader for ~$50, and then go up from there.
Some parts stores (like Autozone) will read the trouble codes for you (in hopes of selling parts). I've even seen a few repair shops who will read trouble codes for free in hopes of getting your business.
Whenever I have check engine light come on, I head to the local AutoZone and have them check it for me. If you can get a competent employee, they can look at the code description and give you some good suggestions. MrShorty is right, of course they want to sell you parts, but you don't have to buy anything. Bottom line, you have a better idea what the problem is! Although, it may take a little trial and error to solve the problem.
I can thoroughly recommend using a CarChip from DAVIS Instruments California. Not only does it read trouble codes and allows you to switch off the engine warning light but it also allows you to monitor all aspects of your vehicle use; speed, rpm, engineload, coolant temp and batt voltage.
It simply plugs on to the OBDII socket.
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