Cycling seems to be the favourite mode of transportation for most people on Usedom island, whether locals or tourists. Especially the flat promenade along the sea coast between the resorts Bansin, Heringsdorf, Ahlbeck and (Polish) Świnoujście is very popular for cycling. Mostly the trails for walkers and cyclers are separate, but sometimes not, especially at the centres of the resorts near the sea bridges - which is a real problem.
It seems walkers hate cyclers and vice versa. In fact, I observed quite some cyclers who did not push their bikes in the pedestrian only zones, but raced through instead. Also, it seems some folks rode a bike for the first time in their life; they were insecure, hardly faster than the walkers and moved in wiggly lines ... on the other hand, walkers mixed up the trails and walked on the bike trail or crossed the bike trail without watching right or left.
More enjoyable were the backroads and cycling trails in the backcountry. The landscape is quite hilly there, so cycling is a bit exhausting, but there's much less traffic there and often you're totally away from car/truck traffic.
Definitely get a map if you want to go cycling in the backcountry. Otherwise you might easily get lost - signs are rare, the hills and lakes make it tough to navigate.
If you want to rent a bicycle you have the option to rent from private shops - cost about 6 Euro per day, but limited opening hours - or to rent from UsedomRad. The latter have about 100 stations all over the island and on the mainland from Greifswald via Anklam to Ueckermünde. UsedomRad is a co-operation with Nextbike - meaning a registration is necessary first (or not, if you are a customer of Nextbike already.) The cost is a bit higher, 9 Euro per day (3 Euro for 1 hour, 6 Euro for 3 hours), but you can return your bike anytime at one of the 100 stations. So you're more flexible. The process is described on a flyer available at any tourist information. Basically you call a hotline, give your credit card number, get a code for the lock and start. Lock the bike and call again when you return it.
I'll admit it: I drove to Heringsdorf. However, I parked the car and didn't move it during my stay. For me, it was the much more convenient and *way* fastest mode of transportation to the island. Schlepping your own bicycle plus luggage on Deutsche Bahn trains, involving several changes, is not really a pleasure ... However, this is more a warning than recommendation on driving to Usedom island.
The roads on the island are mostly (except for the main road along the northern coast) narrow, winding, and often in the woods, meaning dark - high potential for accidents. Parking is a nightmare in the seaside resorts, unless your accommodation provides a place. If you find a parking spot relatively close to the beach or in the centre of the resorts, then it's either for locals or expensive. Even in low season (October) the large parking garage in Heringsdorf, right by the main road, was almost full.
To drive to Usedom take a motorway until you get to motorway A20. Most routes from West or South Germany go around (or through) Berlin. From North Germany take A20 along the coast. When going by Berlin you take exit "Pasewalk" and drive the main road B109 to Anklam, shortly after you take B110 to Usedom. These roads are busy, often go right through villages and small towns, so it takes some time ... (Beware of speed tickets!) If you come from North Germany then you'll most likely leave the A20 somewhere near Greifswald and drive B111 via Wolgast to the island.
The backbone of public transportation on Usedom island is the railway route of Usedomer Bäderbahn (UBB) along the northern shore of the island. UBB is a subsidiary company of Deutsche Bahn. The trains run hourly between the Polish border (Ahlbeck Grenze) via Heringsdorf, Zinnowitz e.g. to Züssow, where you have connections to the fast and regional trains of Deutsche Bahn network (to/from Berlin e.g.)
Every two hours the trains run farther than Züssow - via Greifswald to Stralsund, both worthwile destinations for a day trip.
In Zinnowitz you can change to the trains to Karlshagen, Trassenheide, Peenemünde - the northern part of the island.
Fares are quite reasonable IMO. A single trip within the three "Imperial Seaside Resorts" (Ahlbeck, Heringsdorf, Bansin) was 2 Euro in 2013. Day tickets for bicycles are 4 Euro - valid on the whole UBB routes. Day tickets for single travellers as well as groups are also available, for the island only or for all the UBB routes. The Mecklenburg-Vorpommern Länderticket is also valid. The trains are clean, the service is friendly and reliable, the trains are fast enough - good deal.
If you are in Germany, you can easily go to Heringsdorf by car or by train. And if you're in Poland, you can come here by a tourist ship or a bus, which connect Heringsdorf with Miedzyzdroje (Misdroy) and Swinoujscie (Swinemunde).
The last (first?) stop of UBB is "Ahlbeck Grenze" - just 100 m from border crossing with Poland (Swinoujscie/Swinemunde)
UBB - connects all important cities of Usedom/Uznam Island. Selected trains goes to Stralsund and even to Potsdam.