In Capture the Flag, speed is incredibly important. Players travelling fast can easily outrun or at least dodge most direct shots. The less time it takes an offensive player to traverse the map, the less time the other team has to react, and to run into their base and steal their flag in order to prevent a cap. Defensive players also need speed to be able to catch up to offensive players - a chase defense needs speed to catch up to the enemy flag carrier, and a base defense needs speed to be able to get to his flag carrier fast enough to provide them with support to keep them from dying.
The simplest way of getting to different spots on the map may not be the most obvious: selfkilling. The game provides a way to instantly kill yourself, by typing \kill into your console (or more commonly, by binding it to a key on your keyboard). You will be able to instantly respawn at a random spawn point on the map. These are usually distributed along different routes in your base (no, you can't respawn into the enemy base in most cases). Doing this as a flag carrier is unwise though, since the flag will be returned instantly instead of respawning along with you. But for all other players, selfkilling is an important aspect of the game. Many players will repeatedly selfkill in order to cycle through the different spawn points until they arrive at a favorable one. Keep in mind, you will also lose any weapons, ammo, and shields that you picked up (for this reason, players rarely hoard a lot of ammo at once). However, you will be restored to full health and force points. An advanced strategy is that if you selfkill while holding a picked-up weapon, that weapon will be dropped at the point that you killed yourself at, and can be picked up with as much ammo as it would have if it were freshly spawned (regardless of how much ammo it had left when you selfkilled). This, for instance, is an easy way to keep a constant supply of trip mines as a base defense player.
The next best thing is to use the force. There are two force powers that increase your speed: force speed and force rage. Force speed is by far the more commonly used power, since force rage drains your health while active and doesn't speed you up as much. Force speed, on the other hand, purely speeds you up (and by a lot). Both force powers take 50 force points (half of your overall force points), so you must be very careful about tracking your force point level so that you don't get stuck without the ability to use force speed at a bad time. With enough experience, you will be able to get a sense for when your force speed is about to run out.
The final, and perhaps most important, method of speeding up is called strafe jumping. It is a bit complicated to explain, but due to how the game physics works, by moving in a specific way, it's possible to travel faster than the game's linear player speed limit. In fact, it's possible to exceed the limit significantly, with enough practice. Basically how it works is: step one, "bunny hopping". The idea here is to make your player be always in the air (in which there is no friction), by tapping jump (spacebar) every time your player is about to hit the ground. As long as you immediately re-jump, your player won't incur any ground friction and will be able to maintain any acceleration beyond the speed cap (typically 250ups) indefinitely. The other concept is that, by moving at an angle to your trajectory, you will accelerate, and by alternating the angle on either side, you will accelerate forwards. How this works out is basically that you alternate holding down forward+left and forward+right. Mouse movement is important to maximize your acceleration: when you hold down forward+left, you should face slightly to the left initially and then slowly increase your angle even more left, and likewise for the right side. Here are a few short videos demonstrating the technique: