Taxi - Its very cheap to catch a taxi in Hoi An & its also very safe. Most of the taxi's have meters which makes the whole experience less stressful. Taxi's can be found outside Old Town or you can just wave one down. If you are in a hotel or a restaurant its easy to get them to call.
Rickshaw is commonly used as a local transportation in Old Town. They are extremely cheap & great to use especially if the heat is getting to you. As no cars are allowed in Ancient Town Rickshaws are an excellent mode of transport.
Rent Motorbikes or Bicycle - In Ancient Town its very walkable however if you want to go to the beach you can always rent a bike. Some of the hotels have bicycles to rent or you can rent them in town. However; the roads can be tricky to ride as although it's very pleasant to ride to the beach the road is narrow & basically it can be a little scary on parts.