Ok, its very simple. See, we first have to discover free energy. Clean burning, low cost infinite energy. Thats our biggest hurdle at the moment.
After that, space travel becomes far easier. See, because the object in space is completely weightless, so once you get your initial momentum going, space travel becomes far cheaper. So you dont have to fund then entire trip with energy, but reaching the proper speed is the most expensive part.
Then, you plot the course ahead of time, getting 100+ years of information ahead of time. Steering at that speed is impossible, and your biggest risk isnt aging to death, but hitting something, or getting hit by something. So you have to computer do all the controlling. More plotting can be done along the way, with the ample amount of time you'll have. Once you have all the information and space charts ready, your nearly there!
Now the ship itself will have to be rather large. Because of the infinite energy though, creating, producing, and maintaining things will be much simpler. Growing crops will be far easier, because of the ample space you can have ((no pun intended)) and the unlimited amounts of proper lighting and clean water. Food wont truly be a problem, because you can plant the crops in a rotating cycle, meaning every month you'll harvest one of the crops, for sustainable food.
While you cant get all the vitamins and nutrients you need to survive long trips from just plants, the rest you can tightly pack into bullion cubes, to be melted and mixed into water. Fiber and such are easy to keep in space, because of vacuum packing. Literally putting it into an area open to space, keeping it frozen in time.
While traveling lightyears will still take a generation or two, possibly more depending on speed constraints, you can live a happy life in space because of your lack of worries ((kinda))

Though, you'll probably go crazy from boredom and have to get tied to the wall with duct tape, it could go alot worse!