Visitors to Barcelona will get around easily with the underground, the Metro. However, I will shortly mention how the bus system works in case you want to or need to catch one:
The public buses have a red-white color and the name of the line is indicated in a big display listing the final destination it is heading to at the front of the bus. For example if you have H10 Badal it means it is heading towards Badal.
The bus system has been re-organized just recently. You will see bus lines that start with an H followed by a number / that means the bus travels describing a horizontal line through the town. If it has a V you will travel vertically, meaning either towards the mountain or towards the ocean.
As mentioned before, the T-10 can be used for both bus and metro. You have to validate the ticket in the bus. There are small terminals for that right at the entrance. You can buy single tickets from the bus driver, but not the T-10 tickets, you can buy them at any metro station.
It is safe to take the public buses in Barcelona, during rush hours maybe not so comfortable because the traffic will cause them to move very slowly.
Here you have the link to the bus schedules and itineraries: http://www.tmb.cat/en/linies-de-bus