visit amtrak.com
type in chicago and indy
enjoy 23 or 51 dollar train ride.
That was hard.
Amtrak is difficult because the cheap trains only run at certain times. I've looked in on taking Amtrak on several occasions but the fares were terrible for when I want to travel. All the bus services run more often and cheaper than Amtrak unless you get the $23 special price.
Going to Indianapolis Airport? I honestly don't know of any. There are plenty that go to O'Hare.
Suburban Express, Lincolnland Express, Peoria Charter all go to ORD. The cost varies again on the day and time but it can vary from $20-$40. Peoria Charter is always $20 each way.
In addition, Peoria Charter is the only one I know that still goes to Midway. The others will take you into Chicago and you would have to take the CTA to Midway.
I always fly out of ORD though the bus rides are rather long (3-4 hours) each way. There is a regional airport at UIUC, Willard Airport CMI, but the cost for the connection is pretty high compared to the bus ticket.