There are a number of different options for using the bus and tram here. The tricky part is that there are several bus companies in Manchester and you can't always just transfer from one to the next company. You'll have to pay separate fares. That can add up quickly so make sure you ask the driver which company your ticket can be used on. You also need to keep a close eye on the bus company for another reason. There might be more than one company running a bus on the same route using the same route number!
You can, of course, just pay as you go and pay the driver but you'll need to tell him where you're going. It might be cheaper to buy a return ticket so ask but again, it likely is only good for that same company.
The best option, if you aren't sure and may need to use more than one company, is to get a day saver pass that is good for all companies. You can get a day pass that's good for after 9:30 or all day including peak morning hours. A company called System One is delegated to sell these tickets but you can get these from a driver, a ticket machine at the tram (Metrolink) stops, and train station ticket offices. Not all of the day passes are accepted on trains and trams, though, so ask for one of those specifically if you are going by those routes. Day Saver System One passes are going to cost you between £4 and £4.50 (bus only. passes including the tram, off peak usage, will cost you a couple of pounds more). Other bus day passes, depending on the company, are usually between £3 and £3.50. Here's a general list of prices and companies.
Tram prices depend on how far you're going. Day passes for tram only are also available. You need to buy your ticket on the platform before boarding the train and if you are caught without a ticket, you will be fined.
There are concession, disabled and child fares available and over 60s can get free transportation if qualified.