I was searching somewhere on how far away the nearest star system was and what that system was. Am I correct in that it is Alpha Centauri at roughly 4.75ish lightyears? If so, a probe or ship or whatever we send could reach there in a relatively short amount of time, right? Please tell me if I am wrong.
Current technology can't get us anywhere close to the speed of light (c); the Voyager probes are moving at something on the order of 1/17500 c. At speeds like that, it's about 75,000 years to Alpha Centauri.
There are proposals for small probes accelerated by laser-driven light sails to speeds on the order of 15% of light speed -- 25 years to Alpha Centauri -- but there are a large number of engineering challenges in building such things that we haven't even begun to solve.
The JHUAPL Interstellar Mission proposal uses minimal development of current technology (mainly qualifying a large solid upper stage) to achieve a speed 4x higher than Voyager, so on the order of 18750 years to get to Alpha Centauri.
The British Interplanetary Society has spent some time looking at this, first with Project Daedalus 1973-78 taking 50 years to flyby Barnard's Star (5.9 ly) and in a high degree of technical detail in Project Icarus 2009-14 which spawned the Initiative for Interstellar Studies - i4is.org
Numerous papers have been published as a result of this work.