This really depends on the country, but there are broad patterns worth knowing. Most large cities worldwide run some combination of buses, metro or suburban rail, and increasingly trams or light rail. Buses are the near-universal backbone because they need no special infrastructure, while metros exist mainly in bigger or wealthier cities.
Coverage is where the real variation shows up. In much of Europe and East Asia, networks extend deep into suburbs and even small towns, with trains connecting rural regions. In North America, Australia, and many developing countries, coverage outside city centres can be thin, and a car or shared taxis become essential. Rural areas almost everywhere rely on infrequent buses, minivans, or informal transport.
Before you commit to housing somewhere new, spend time on the local transit authority's route map and test the commute at the actual hour you would travel. A place that looks connected on paper can feel very different with one bus an hour.