Busses of the Hamilton Street Railway run on a number of different lines. According to the outline of the city, most run either east/westbound, or south/northbound between upper and lower Hamilton. So getting from any point of the city to Upper Hamilton for example requires a transfer downtown.
Tickets are $2.55, and you have to have the exact change on hand - drivers don't carry any change, the money is collected and counted by a machine. The other alternative is to buy five discounted tickets for $2 each at stores like Shoppers Drugmart or cornerstores, or a monthly pass. If you need to transfer or plan to take a ride back soon, make sure to get a transfer ticket, which is valid for 2.5 hrs, and can be used on any bus on any direction.
Service hours depend on the route; some are operated untill about 2am.
Apparently there is also the option to get a transfer to the Burlington bus, but I don't quite know how that works since I have never used it.
Also, there are plans to implement the "presto"-system, which allows you to pay your fare with a contactless smartcard. As of Dec 2010, they are not operational yet. Once in place, the cards can also be used in other cities with the presto-system, such as most of the neighbouring towns and Toronto.
There are four trains daily from Toronto to Hamilton, all during the evening rush hour. These are, of course, commuter trains and are usually quite packed leaving Toronto. At that time of day, though, they are the best option.
At other times, you'll take the bus. It leaves from Union Station, costs $16.40 return and takes anywhere from 50 to 75 minutes, depending on traffic.
They leave every 30 minutes, and more frequently during peak hours.
Driving is easy in Hamilton, except there are too many one-way streets. It's confusing to visitors. There is bus service in Hamilton too, but it sucks. A lot of routes only have service every 30-60 minutes even during rush hour, and no night service. Plus, buses are very slow. It takes too long to get anywhere by bus.
HSR!~ You can take the bus everywhere!! Buses in Hamilton are very frequent and if you don't know your way around this is the best bet. Most streets in Hamilton (especially downtown, where I would say all) are ONE WAY which can be a big pain if you are just visiting and trying to get somewhere.