The majority of travellers arrive by ferry or bus to the port. If you are coming from Taba/Cairo you could ask the bus driver to let you off by the hospital. From the port you'll have to find a taxi to the city or Tarabin. It should not be more than 5-10 LE, but as taxis are often scarce, prices will be inflated. Negotiate hard.
Between the city and Tarabin distances are coverable by foot. If you're let off by the hospital it's a twenty minute walk to the beginning of Tarabin.
There are only a few ways that you can get around in Nuweiba. One is the blue and white taxis. Although you can get just white taxis, stick only to the blue and white and also try and make a mental note of the drivers taxi license, which should be on clear display, and his taxi number, which should be on the drivers side of the taxi. If the driver is good and charges a good price then try and take his number as taxis can sometimes be hard to come by in a small place such as Nuweiba.