Artificial gravity isn't that hard to achieve. The only thing necessary for this gravity is a round, cilinder-form shape of the spacecraft. The gravity can be made by spinning the spacecraft in a consistant speed in lenght around it's own axis. All inside loose objects will clamp to the inside wall due to the artificial atmosphere that is created inside the spacecraft for breathing and, well, living. The same thing happens when you spin a bucket of water at the same speed around. Momentum and Newton's 1st law makes sure that the water stays in the bucket.
The travelcourse, on the other hand, is a little bit more complicated. First this spaceship needs to create an orbit around the Earth before setting up course to Mars. For artificial gravity to be created we need quite a long ship. This is a complication since the longer or bigger the ship is the heavier it will be and the more fuel you will need. When we do make it to a full and succesfull orbit, chances are high that we don't have any fuel left. This, ofcourse, can be easely solved be sending more fuel op there (but is really expensive). If we do have the ability to refuel, we need to make a calculated burn to enlargen our orbit shape into a very long oval shape that intersects Mars' gravity field. This burn will use a lot of fuel. When we get in that gravity field we need te make another burn to get into orbit aroud Mars, again, this uses fuel. When in orbit we still need to make a soft, succesfull landing. By turning the spaceship retrograde (oppesite side of course direction), burning, make the orbit smaller and get closer to Mars until we enter the atmosphere. More fuel is used.
At a speed of about Mach 2 or Mach 3 even (1 mach = speed of sound = approx. 1320 km/h) we can't say we can make a soft landing. By again burning retrograde we slow down by a big amount and are able to land softly while using landingstruts and parachutes.
This journey would take about 10 - 15 years, billions of dollars, billions of gallons of fuel, and a lot of smart and patient people.