If you are talking about an interstellar mission to another star - rather than interstellar space itself - there have been ideas for that. Originally Project Longshot and Project Daedalus in the 1970s
Project Daedalus 1970s Artist's Impression of an unmanned interstellar spacecraft. It was going to use helium 3 mined from the atmosphere of Jupiter over a 20 year period, and would take 100 years after that to get to Alpha Centauri. See Project Daedalus
The idea was revived again in 2008 as Project Icarus (interstellar). They hope we will be able to send a mission which will take 100 years or less to get to Alpha Centauri (similar to Project Daedalus) and launch it before 2100. But with the idea that perhaps that could be speeded up also through technological innovation.
And the most imminent of their proposals is Project Tin Tin | Icarus Interstellar to send a fleet of nano satellites to Alpha Centauri, which hopes to launch them before the end of this decade.
There are many other ideas for interstellar flight, using solar sails, MagBeam , particle beams etc - but the interstellar cubesat is probably the most imminent.
With laser propulsion, you have a high powered laser back on Earth or elsewhere in our solar system (e.g. Jupiter) which fires laser beams at the spacecraft to accelerate it.
One interesting twist on laser propulsion is the idea of sending beams of particles instead of light to accelerate the spacecraft. Once you have particle beams, you also have the possibility that they could steer themselves towards the receiving spacecraft, which is Nordley's 1999 "BeamRiders" idea
The nearest known star is Proxima Centauri actually, a red dwarf with no known planets as yet.
Anyway it is 4.2 light years away. So - unless we find a way to travel faster than light - if we could send a probe at the speed of light, it would be 8.4 years before we got data back. At a more likely a tenth of the speed of light or so, you are talking about around half a century before you get the first data back from first launch.
Of course, there's also the intriguing question of whether there are any as yet undetected stars closer than Alpha Centauri.
Brown dwarfs especially - stars so dim they are just warm, a bit like Jupiter would be if there was no sun around to illuminate it - but with occasional sporadic fusion inside - they could easily be closer than Alpha Centauri and not yet detected. Search for Brown Dwarfs on centauri-dreams.org