With a code reader. Have your local auto parts store read the code(s). They provide this service for free.
In US it says "SERVICE ENGINE SOON" in Canada it looks like an engine.
If your Chevy trailblazer 2004 gauges are not working, check your fuel pump.
There are pages and pages of things that can cause a check engine light. You need to have it checked with a scantool. Then the code can be diagnosed and repaired.
Check
check cat converter if it has 75000 miles or more
The check engine light sets a code for diagnostics and you need a code reader. Most auto parts stores sell code readers and most will check the codes for free.
The check engine light (service engine soon) comes on and stays on when a problem is detected by the self diagnosis system of your vehicle.
First check the fuses.
Check the fuses first
Get the Trouble code read then have it reset at the same time. You can also disconnect the negative battery terminal for 10 minutes and it will reset. If you have not fixed the problem the code will set again causing your check engine light to come back on.
It sounds like your fan clutch is bad.
Take it to a local PepBoys they can scan if you have a check engine light on and from there I can help you more with diagnosing a misfire incase you have multiple problems