Public transport
Public transport in Barcelona is fabulous and cheap and since we walk or ride everywhere we no longer feel the need for a car. There are tubes, bicing, trains and buses and all run very nicely thank you.
Barcelona has to have one of the best public transport systems anywhere, and even if you're travelling by car, roads are generally well planned and well thought out (although there is still a lot of congestion on the main Rondas at rush hour). For instance we live just next door to a motorway, but you wouldn't notice as there's a park running over the top of it, so it's never seen.
The difficulty as with any public transport system is working it all out in relation to the bits of the city you know and the bits of the city you might want to go to, but it's really worth the effort as it is clean and efficient with high quality bus, metro, tram and train journeys.
Tickets
Elsewhere we've mentioned about using a T-10 multi-personal ticket if you are trying to get around the city. You can use it for several people on the same journey (put the ticket through the barrier for each person in your party). It makes travel extremely cheap.
Renfe, Metro and Cercanias, FGC
There are lots of options for transport, but it can be a little confusing to start with. TMB has maps available and full details of routes including buses.
Renfe is the Spanish national railway company. Renfe runs the medium and long distance trains for instance to Girona or down to Tarragona.
Closer to home Barcelona has its own local rail network called the Cercanias. You can find details of the local trains on the Renfe website in a special section, but not off the main list.
Obviously then there is the Metro which just works in the city and includes trams. There is also the FGC which is separate from Renfe and runs from Placa Catalunya and Placa Espana up to Sant Cugat and the hills at the back of the city.
Finiding stations
If you are travelling out of the city to other places, trains travel through a number of stations in the city - almost all go through Sants which is rarely the most convenient place to start or finish a journey, but you can usually also pick up the train in 2 or 3 other city stations as they pass through - for instance Passeig de Gracia, or Arc de Triomphe. The effect is that you don't have the madness of trying to get to a crowded terminal station to start your journey (the only formal terminus is Franca which has relatively few trains using it, but is also home for the airport train).
The only problems or confusions we've had are normally on interchanges. For instance Passeig de Gracia is both a metro and a train/cercanias station, but we find ourselves struggling to find the train bit of the station from the metro passages. It almost seems that you have to go above ground to find out just exactly where the train station is, and occasionally you need to enter through the main entrance .
Another example is Placa Catalunya - the station covers a large area under the square, but there are separate entrances for metro and RENFE train (though they join up underground). However, if you want to use the Ferrocarrils Generalitat de Catalunya (FGC) lines that run up to Tibidabo, Sarria and the hills at the back of Barcelona, you need to go overground to the corner near Cafe Zurich, opposite the Ramblas where you'll find the FGC specific bit of the station.
Buses
The other thing to mention is buses. In many situations the metro routes can look very tortuous to get from one place to another. However, where the metro journeys are difficult there is usually a bus journey you can use instead. Buses are very clean, very modern and very comfortable. A for instance - if you want to get from the beach to Park Guell there is a bus that will do that route.
Cars
If you do choose to use a car, the first thing to note is that all the car parks tend to be underground (and are very difficult to spot unless you know where to look). There is above ground parking, but locals say it's risky as the car is likely to be scratched or bumped by passing traffic on busy streets. The second thing is that in the grid system for Barcelona most streets are one-way and 3 or 4 lanes wide. It can be terrifying trying to navigate looking for the right turn into the right street with cars and mopeds flying around you whilst watching out for traffic lights and other obstacles. I hired a car from Sants station and it turned out you pick the car up at the top of the station, drive down a ramp and are immediately in a 6-way road seemingly in a middle lane.
The final little thing with cars is that if you are turning left or right on a traffic light controlled junction, there is probably a zebra crossing with a flashing light just around the corner. Your green light is on the same phase as the green man on the side streets, so turning off expect to have to stop immediately around the corner.