The cheapest way to get to the island is by using bus connections, which connect from Cancun to Chiquilá.
You can take the bus from the Cancun Bus Terminal at 7:30 am, 12:30 pm and 1.30 pm (the last is the third class) for approximately 6 USD per person.
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.