You didn't inquire about Barcelona. Will you be there for a time, if so, getting around Barcelona, as others have said about the other places you mentioned, is easy and inexpensive. The metro is Barcelona is well marked, but if you prefer to travel about ground the bus system in Barcelona is among the best I've ever experienced. You can even download a map of the entire bus system in Barcelona, and plan your route(s) to various places you want to visit right from home. There is also an internet site enter link description here where you can understand the railway routes between/among the places you'll visit. Don't fret about transportation, enjoy your trip.
Unless you've already made hotel reservations for the order of cities you'll visit, and unless your flight into Madrid and out of Barcelona (you didn't you had a flight out of Barcelona, but I'm guessing this is the case), you might want to start in Barcelona, then Madrid, then Granada, then Seville. Or alternatively, arrive at Seville (probably no international flights, but get one from where ever your "gateway" is), then visit Granada, then Madrid and then Barcelona. Just an observation.
There is another great source for maps on the internet enter link description here When you open the map, you'll be in the US, just use the mouse to "Europe", then zoom-in using the "+" key. You can make your own maps of Barcelona, Madrid, Grenada and Seville. If, when you're in a city of your choice, go to the icon that looks like layers, and click on "transportation" and you'll get an idea of where buses run. Note that the bus route numbers could be a bit "off", but you'll get a general idea of how to navigate each city with buses. The maps usually show Metro/subway stations, but not the underground routes.
Hope you have a fun time in Spain.