If you can speed your ship up to .99c (almost the speed of light), then you can reach the closest star to the sun in approximately 44 years (give or take some time to account for the acceleration stage)
Anti-matter would work more efficiently, as it converts all the matter used into energy but it is very hard to produce, and there is only an estimated 20kg of antimatter floating in the solar system today.
A theoretical way, is to prove that tachyons exist (particles that always travel faster than the speed of light), and somehow use the same method to travel faster than light. This may not work as these are purely theoretical particles, never found in the lab or nature.
Another way, is to figure out quantum teleporting or space-time warps. Quantum teleportation is a very real thing, quantums (particles smaller than atoms) can simply jump from one place to another without accelerating or moving at all (except their final location of course). If you could build a space ship that utilises quantum teleportation, you could get anywhere incredibly fast.
Space time warps, if they exist, are parts of the universe in which there is a deformation of space-time which could let you travel faster than your actual speed relative to the universe if you went through it (for example, if you were travelling at the speed of light for 1 day in the space time warp, then where you come out may be a location that would normally take you 2 days to get to).
A theoretical example of a spacetime warp that could be utilised for use as a worm hole (to get faster to places), is a black hole. If you could fly through a black hole, then you would go back or forward in time, essentially saving you time)\
I know its long but I hoped this is what you were looking for