By ship
Ferries
There are hourly rides to and from Playa del Carmen, costing about 156 pesos $13.50 USD per adult each way. There are two companies, so buy a single ticket because you may need to use the other ferry company coming back and the tickets aren't transferable two one-way tickets cost the same as a return anyhow.
A car ferry leaves from Calica, a few kilometers south of Playa del Carmen pass Xcaret. The car ferry from Puerto Morelos no longer exists! There are 4 ferries each day, but the first at 04:00 AM and the second at 08:00 AM are specially for supply and logistics of the locals and islander. So take the ferry at 12:15 AM and 06:00 PM. From Cozumel back to the mainland you can take all ferries: 06:00 AM, 10:00 AM, 04:00 PM and 08:00 PM. It should be noted that rental cars are not allowed on the car ferry and you wouldn't want to do it in any case as taking the car ferry is a huge hassle involving a lot of waiting on both ends. Not recommended for anyone on a one to two week vacation.
Cruise ships often visit the island. A few can dock virtually downtown. A larger pair of piers lies about two miles south of downtown San Miguel, and primarily serves Carnival and Royal Caribbean Cruise Line ships. If many ships arrive the same day occasionally in "high season", some may moor offshore and tender passengers to docks virtually downtown.
By plane
Cozumel has an international airport Airport Code: CZM which receives direct flights from Atlanta, Charlotte, Chicago, Dallas, Denver, Halifax, Houston, Miami, Minneapolis, and Toronto as well regional flights from Mexico City.
Alternatively, you can fly into Cancun Airport Code: CUN which generally has more flights, then take a bus or van south to Playa del Carmen and take the ferry across to Cozumel. A shared van from Cancun airport to Playa Del Carmen will cost around 300 pesos per person one-way, where a bus will be around 130 pesos or $12 USD if you do not have pesos handy per person one-way.
You can buy online your transport in advanced. Here are two companies:
Amstar DMC (http://www.amstardmc.com/...) offers private and group Airport Transfers
Gray Line (http://www.graylinecancun...) shared cozumel shuttle.
Also you can take a small plane to Cozumel from Cancun airport's domestic terminal. It takes just 15 minutes and the trip is an amazing experience for about $75 USD per person one way.