The cheapest way is to take the NORTH exit out of the airport and then go WEST on TOLL 528 (Beachline Expressway) to I-4. Then take I-4 WEST to the next exit which is SR 535 (Lake Buena Vista/Kissimmee) and turn right to go NORTH on 535. At the first traffic light you'll see the big Disney World welcome signs and you turn left there to go WEST on Hotel Plaza Blvd and Downtown Disney will be straight ahead of you in less than a mile.
Slightly more expensive and a few minutes quicker (especially during peak times on I-4) is to take the SOUTH exit out of the airport to TOLL 417 (Central Florida Greeneway) and go south on the 417 to the exit with SR 536. Follow 536 west and you'll cross over I-4 and enter WDW. The first exit after I-4 is Buena Vista Drive where you would turn right, proceed less than a mile and Downtown Disney will be on your left.
The colorful Disney road signs clearly mark "Downtown Disney" and are easy to follow.
The Downtown Disney parking lot has major renovations going on because of the addition of a T-Rex Cafe. Parking can get scarce (or distant from Marketplace) during peak times!
BobK/Orlando