O'Hare International Airport (ORD), Midway International Airport (MDW)
You can fly into either Chicago airport for Lollapalooza. Midway is the smaller of the two, but has Southwest and is often the more pleasant option. Regardless, either option is an easy trip into Chicago. From Midway you can take the Orange Line L Train for $2.75. Into the city will be about 30 minutes. To get from O'Hare to Chicago you will also use the L-train but it will be the Blue Line. Again it will be a $2.75 charge for a one way ticket and will be about a 40 minute ride from the airport to Chicago. You can Uber or Lyft from the airport to the city, but I highly recommend just using the train.
$2.75 each way from either airport to the city
Generally the cheapest time to book flights for Lollapalooza will be about six weeks before Lollapalooza. This means you should be focused on booking your flight in June 21, 2018. This may seem late to you planners out there, but statistically it's the cheapest time to book flights. That said, if this is too late for you book it earlier. One final note is that plane tickets for Lollapalooza tend to skyrocket about two weeks out, so certainly don't wait that long to book a Lollapalooza flight.