The easiest way is definitely to go by taxi. If it's not rush hour, probably the quickest as well. However, that's certainly not going to be the cheapest way. From Midway airport, the orange line runs directly to downtown into "the loop" where all the lines circle part of the city. You can take the blue line from O-hare to the loop. Transferring in the loop is easy and can get you to some of the more outlying hotels north of the river. To get to the Hyatt by the convention center, you can transfer from the orange to the red line heading toward 95th and get off at the cermak/chinatown exit. It's about 3/4 mile walk to the Hyatt from there. The orange line is about 40 minutes to downtown from Midway and the Blue line is about an hour from O'hare.
Average cab fare is probably about $25 from Midway to downtown and $40 from O'hare. (These are guesses verified by a quick google search to see if I'm still in the ball park.)
The CTA is 2.25 for a ride. Pro-tip -- you can get passes at various places (pretty much any walgreen's or CVS and probably any grocery store in the city). Three day passes break even at about 6 rides, and seven day passes at about 10 rides (Elevated train or busses). If people are taking the Metra (different from the CTA) from downtown to the Convention center, save 10 percent by buying a 10-ride ticket.
Pertinent websites are transitchicago.com and metrarail.com. Googlemaps is the best for planning public transit trips in Chicago. It requires learning least about the system.
Hope this is helpful,
See you in Chicago!