The best way I can think of to describe Cirque Shanghai is that it is a less elaborate, and way less expensive version of Cirque du Soleil. It is a fun, amazing, awe-inspiring time.
Cirque Shanghai performs at the Navy Pier every year starting late May and ending early September. This year Cirque Shanghai will be at the Navy Pier until September 3rd, so, you only have a month left to see them perform this year.
A basic ticket is around $20 dollars; for more money you can buy an "Emperor's Court" ticket which will get you a better seat. If you are going to an evening show during the week and buy your ticket early in the day, chances are even a basic ticket will get you a good seat.
You can buy your tickets through Ticketmaster or in person at the Navy Pier box office. I highly recommend the in person route as that will save you approximately $6, or more if you choose to buy Emperor's Court tickets (in person basic tickets are $23 with tax, basic tickets at Ticketmaster are $29 with taxes and fees).
Below is Cirque Shanghai's promo video for their 2012 show.