Manchester Airport (MAN) is about 10 miles south of the city center. The easiest and quickest (30 minutes) way into the city is hailing a taxi (£15); or, you can hire a private taxi in advance. You can also take a train to Oxford Road and Piccadilly stations by going to the Skyway between terminals 1 and 2 (£3, running every 20 minutes). Three buses run to the city center, with the 43 and 105 being the most direct and the 44 taking a little longer.
John Lennon Liverpool Airport is less than an hour away from Manchester, making it a viable alternative if you cannot find good flights into Manchester Airport.