Many players start playing Star Citizen from entering Hangar. They think that it's starting point of the game. They launch it, come close to the ship, enter it..But they have troubles with leaving their Hangar. That’s because they don’t know that right now Hangar module doesn’t allow flying in space. When you are in hangar you can walk and enter your spacecrafts but you are not able to fly! In future Hangar will be connected with core game but now it’s an independent module.
If you want to fly you need to select another game module, Arena Commander for example. This module allows fighting against other players. In order to do this press Esc key while you are in Hangar (you will see main menu), then click Electronic Access and select the module you wish to launch. Right now Arena Commander is the only module. Select what game mode you wish to play: with friends, solo or training. You are done. Now you can use your spaceship.
You can also explore the space in Universe mode. This mode allows you to play the game with other players. It’s similar to MMO. When you are in Hangar press Esc and select Universe in main menu. You will appear in a large spaceship (base). This is your starting point. Travel, trade and do other stuff you wish.