These are primarily utilised by low and middle wealth sims to commute to work in commerce or industry or to shopping. You'll get prompted by the game when it feels you need to add a bus station, no point in adding one before due to the costs involved in running a successful bus operation as as well as the bus station you'll need to add numerous bus stops and multiple busses. As well as stops and busses you can also add park and ride blocks.
The bus station also acts as a bus stop and is best placed near lower wealth residential zones. High wealth sims don't really have a desire to use buses nor are too impressed by you zoning bus facilities close to them.
So you've found a good place for your bus station, now think about adding a couple of park and ride zones, these are facilities for lower wealth sims to drive to to then catch a bus ftom, so make sure you plop a bus stop close by to each one. You can see the catchment area of each park and ride zone by the green shading over the roads.
Now it is time to plan your bus routes, try to cover most of your map, and even place bus stops on both sides of the same street so your sim is covered both ways and doesn't get stuck at the shops or something weird. Bus stop coverage is indicated by the green strips along the road, darker/brighter green indicating better coverage.
Later in the game you may want to consider adding a Municpal Bus Garage which provides a bus service to and from other Cities in the same region as you, this is good for travelling commuters, tourists and shoppers. This garage also provides services for Sims within the City and are a good supplment to the ordinary Bus Station.
Adding a Municipal Bus Garage
These require a substantial investment to get going basically because you'll need to upgrade all your avenues (or rebuild your roads into avenues then upgrade them) to high density Street Car roads, then add your street car station, street car stops and fleet of vehicles. All in all, to upgrade a full road network in a city and add the facilities, you're looking at an investment of around 300,000 Simoleans. So only go ahead if you are sure you have the Simoleans and your City can afford to take on the extra burden of a new transport system on it's finances. It's better to wait until you have good revenue streams coming in and at least around 50,000 sims in your City in my opinion. You can always just upgrade your streets to high density avenues to take the strain off your road network before upgrading again to high density street car avenues and then eventually rolling out your fleet of street cars and stops.
They will help your Sims get from A to B and form an integral part of the mass transit system within any sucessful City, but make sure you are ready for it, and don't make it a white elephant vanity project that brings down your City. Remember you sims can use all forms of mass transit so they may want to get a bus to the shops, before taking a street car to back home again or vice versa. Street cars mainly appeal to lower and middle wealth sims.
Trains are only really useful to connect one City's sims to another City and vice versa, if there are no other acive Cities in the region then this negates some of the train station's udsefullness. However it is useful to be utliised in conjunction with of the trade port upgrades which allows you to ship freight to the global mass market via train.
Considering their huge footprint on your map, this is not a great option for most cities, unless you are really looking for heaps of tourists and are pursing cultural goals.
Upgrading your Mass Transit Services
So, the likeihood is you have started a bus service in your City. As you progress in to the game and your City's population increases, you'll need to either improve yor bus service (assuming you started one!) or add a Street Car service.
Depending on your finances you'll make the decision to do one or the other once your mass transit alert starts going off indicating your current level of service is becoming insufficent.
Option 1 - Improve your Bus Service
This is the cheapest and simpleist option to take, you can either add a second (or third) bus station or a municipal bus garage, this has the added benefit of even more busses and starting a regional bus service which will transport your Sims from one City to another in the same region, and also help bring in commuters and visitors from other Cities in the same region to yours, which is great for commerce.
You'll want to double check you have enough park and ride slots and enough bus stops on both sides of streets.
Option 2 - Start a Street Car Service
This is not something to be undertaken lightly as it can cost a bomb to upgrade your roads to handle Street Cars and to actually run a good service, it is something that most Cities will eventually strive to achieve in the game so you can feel free to take you time before undertaking a massive road upgrade program to accomodate Steet Cars.
Upgrading Roads to Accomodate Street Cars
There are four main methods of mass transit available to you in Sim City; Buses, Street Cars, Trains and Planes. Planes and an airport are not really suitable for most cities unless you are specialsing in a cultural tourist driven city, trains are great to bear in mind later in the game for trade and if there is a second City in the same region as you as this will connect commuters and tourists from one city to another int he same region. But the forms of mass transit you'll probably utilise first will likely be busses and later street cars.