My check engine light came on in my 96 honda civic dx coupe Friday morning on my way to school. It was cold and I didn't give it time to warm up because I was running late. It was a very bumpy ride to school but drove home fine. The light came on as soon as I started it. It has only traveled about 3 miles since the light has came on. What are the possible reasons for the light to come on if I can't tell what the problem is and it seems to be driving well?

There are a lot of possible reasons. 96+ Civics are OBD-II, which means they have to be connected to a computer to read out error codes. Just take it to a shop and ask them to read out codes for you. It will tell you what error caused your check engine light to turn on.

How much does it cost typically for a shop to look at it?

I have no idea about prices in USA. In Croatia, some mechanic shops will do it for free, others would charge about 15$-20$.

U have obd2 (96+ )so you can take to autozone and they will do it for free if u do take it to a shop they will get u for about $30-$80 just my 2 cents