No need to do anything other than walk within the city, though it is strongly advised not to be walking around at night for your own safety.
There are plenty of taxis. As always, negotiate a price before getting in most fares shouldn't cost more than a couple of dollars. It's a good idea to get the mobile phone number of one for emergencies. Always agree a price before you get in the car.
Local transport around Kilimanjaro can be easy if you take local buses called "Daladalas". They are 16 seater minibuses which usually transport about 30 people and/or children and livestock at any given time. Daladalas can be used to go within Moshi or to the surrounding villages, for instance Machame and Marangu, and are very cheap less than a dollar. Listen to the conductor shouting the destination as they drive past, and feel free to shout your destination to him. They sometimes have stickers in the front window stating where they go to. Local transport should cost between 500/= and 3000 /=. It's not recommended to travel by daladala or by taxi up muddy tracks if it's been raining very hard. It's also essential to check that the vehicle is in a reasonable state of repair and that the driver is sober.
Motorcyle taxis Boda bodas are numerous but are the most dangerous way to travel. Helmets are not available for the passenger. Many drivers are quite reckless and numerous incidences of drivers taking passengers to remote areas to rob/rape have been reported.
To hire your own Land Cruiser and driver is around 100,000 TSH a day.
