Suggested methods of Interstellar travel, and how well they work with modern physics.
1.) Slower Than Light Ships (STL) - basically, keep going until you get there. Just don't mind the years long travel time to the nearest star system. This would work, although don't plan on a round trip.
2.) Hyperspace - There's actually two different forms of hyperspace, although both work similarly. The first one is the one seen in Star Wars. Basically, the ship jumps to an alternate dimension, usually referred to as Hyperspace, where it is somehow able to travel at a much faster rate than it can in the normal universe. Locations in hyperspace correspond to locations in the normal universe - thus traveling 'X' distance in one direction in hyperspace will always take you the same distance and direction in the normal universe. Is this possible? Ask again when we figure out how to travel through other dimensions.
3.) Teleporting - this is often referred to as Hyperspace, as well, although it works slightly differently. In this varient, a ship uses the Hyperspace dimension to basically shift its location from one point to another almost instantaneously. Battletech uses this method, as does Freespace (although the latter refers to it as Subspace, and only uses it for in-system movement). Once again, ask about this when we figure out how to travel to other dimensions.
4.) Wormholes - Sometimes referred to by other names. Basically, a tear in the fabric of space that allows a unit to travel from one specific point to another much more rapidly than it ordinarily would be able to do. Sometimes the travel takes an interval of time, and sometimes the travel is instantaneous. The wormhole in Deepspace 9 is an example of this, as is the Starfire setting. Wing Commander and Freespace use this form of movement to travel between different solar systems. Theoretically possible, although whether its practical or not depends on how common wormhole type objects are. In Star Trek, they appear to be fairly rare, while in Wing Commander, Freespace, and Starfire, most systems have at least a few.
5.) Real-space Faster Than Light (FTL) Drives - using this system, the ship is able to go faster than light while not using wormholes and jump. Star Trek uses this form of travel with its warp drives. Unfortunately, according to physics as we understand it, this form of travel is impossible. An object cannot travel at the speed of light, meaning that we must always remain at a slower speed. Note that this doesn't necessarily preclude objects from traveling faster than the speed of light so long as those objects never travel slower than the speed of light (such fast objects are known as Tachyons). Star Trek gets around this by claiming that the Warp engines 'warp' normal space, allowing the ship to cover more of it faster.
There are other variations, but most of them fit one of these categories.