Halifax only has bus and a passenger ferry for public transportation at the moment. The bus network is fairly good and will take you most anywhere you need to go. Some routes are less busy and only run hourly but most run on a 20 - 30 minute schedule, some more frequently during morning and afternoon rush hours. Schedules and route maps are here on the Metro Transit website.
There is an Access-a-Bus service for disabled passengers (you must register) and many of the regularly scheduled busses are low-floor accessible busses that have space for up to 2 wheelchairs.
The busses are in the process of having global satelite systems installed and there will be a real-time schedule that you can see on screens at central points or hear over the phone from each stop. It's called GoTime and that's available now but it just gives you the next scheduled bus. If the bus is late, it won't tell you that yet, but it will do. Each bus stop sign has a number on it to call.
Busses currently (2010) cost $2.25 per trip. The driver does not make change so you must have the exact amount. Seniors, children and students cost less. Students need to have ID. You can then ask for a transfer and will be given a slip of paper, colour coded by day. Show that to the driver of the next bus. Transfers are good for about an hour and a half. You can use the transfer to return on the same bus you started out on. Transfers are also good for the ferry.
There are three express routes as well, though more are planned. One goes from Cole Harbour in Dartmouth to downtown Halifax, one goes from the Woodside ferry to the Cole Harbour terminal and the other from Sackville to downtown Halifax. They cost an extra 50 cents on top of the regular fares but there is no reduction for students, only seniors and children. The Woodside route only runs at morning and afternoon rush hour to coincide with the Woodside Ferry which also only runs during morning and afternoon peak on weekdays. The other two only run weekdays but run all day. You can get a transfer to another bus or the ferry and you can use a regular transfer plus 50 cents to get on one. These busses are air conditioned and have comfy seats and because they are called "MetroLink" you will often hear people calling it The Link for short.
There are no day passes available at this time but you can buy a monthly pass which is good for a calendar month, i.e. June. These are available from about the 20th of the previous month until the middle of the month they're for. There is no reduction for buying it after the first of the month. It costs $70 for an adult, less for seniors and students. Students must display the pass with an id. A Metrolink pass costs $85 with no reductions for seniors or students.
Tickets can be purchased for $18 for an adult and student (cheaper for children or seniors), this is a sheet of 10 tickets. They can be used on the MetroLink plus 50 cents. Use a ticket, ask for a transfer as above.
Another service that Metro Transit offers in conjunction with the Downtown Business Association is FRED which stands for Free Rides Everywhere Downtown. This is a free, low floor accessible shuttle that runs a circular route around the downtown core between the casino on the north end of the downtown area to Pier 21 in the south end. It goes up to the fortress on Citadel Hill and up Spring Garden road to the Public Gardens as part of it's route. find out more information and a route description here.