You should watch The Expanse, a very good TV show.
Their ships accelerate at a comfortable level to generate gravity for half of the destination, and then "flip-and-burn" by accelerating in the opposite direction at the same comfortable level to generate gravity.
That only works inside the solar system. The energy requirements to accelerate for a year are enormous. With 100% efficient engines, you would need something like a reaction mass the size of Jupiter.
On the plus side you quickly approach c. At constant 1g acceleration / deceleration, Andromeda is about 28 years away.
Right, the people onboard the spaceship will only perceive 28y to have gone by. People on Earth will perceive the spaceship accelerating away for millions of years.
The ISS weighs 440t and to get 1g there by acceleration you'd need to constantly apply a force of ~4.4MN (meganewton), that's a tenth of a Saturn 5 at lift-off.
Not sure we can do that for an extended amount of time (read: a few hours) without bringing along lots of fuel
That or we invent that special drive of that dead Martian.
Their ships accelerate at a comfortable level to generate gravity for half of the destination, and then "flip-and-burn" by accelerating in the opposite direction at the same comfortable level to generate gravity.