If you rent a car, you must use the "180" toll-free road to Merida (Libre) and the easiest way to get it is going out from the Airport, going to Puerto Morelos, then take the road to Leona Vicario and now you are on the toll-free Libre.
Going straight on till Valladolid Nuevo, turn right and go on for 22 km (14 miles) and then follow the road signs to Chiquilá. It’s very easy!
The total distance is 180 km (110 miles) and takes about 2 hours and 30 minutes to drive. 
In Chiquilá there are several parking lots where you can leave your car for about 5 USD per day.

Once you arrive at the Port of Chiquilá you must take the collective ferry that connects Chiquilá to Holbox, which costs 70 Mexican pesos per person. 

Ferry schedule:

Chiquilá to Holbox: 6.00 - 8.00 - 10.00 - 11.00 - 12.00 - 13.00 - 14.00 - 16.00 - 17.00 - 19.00 - 21.30
Extra connections: Mon-Tues 7.15 / Fri-Sat-Sun 18.00 / Sat-Sun 15.00

Holbox to Chiquilá: 5.00 - 7.00 - 9.00 - 10.00 - 11.00 - 12.00 - 13.00 - 15.00 - 16.00 - 18.00 - 20.00
Extra connections: Mon-Tues 6.30 / Fri-Sat-Sun 17.00 / Sat-Sun 14.00

Alternatively, only during the day, you can take a private boat from the Port of Chiquilà. The price is approximately 40 USD.