Unless you’re taking a ferry from Tanzania’s capital, Dar es Salaam, you’ll be flying into the Zanzibar’s Abeid Amani Karume International Airport (ZNZ).
Despite construction of the new terminal, started in 2011, as of 2017 there is still only one old terminal in operation and it is really small. Quite likely, the first things to do would be getting a visa, money and local SIM Card for the Internet.