As jhocking mentions, a good place to start would be to find your own style and adjust your technique. Some feedback is great at this stage, you can show your drawings to your friends and ask for their opinions, or share them online in places like DeviantArt or similar.
I also agree with the traditional first approach. You can go digital in a next step, but nothing will give you more experience than actually using pencil and paper. When you are ready and happy with your technique, you can start experimenting with Photoshop, Illustrator or similar, which will be absolutely necessary if you want to start working as a concept artist.
There is no typical career route to becoming one. Some may start their careers as Graphic Artists, Illustrators or Graphic Novelists; others have worked in Special or Visual Effects or in Animation, and make the transition to Concept Artist via storyboarding. There's no special training or qualifications needed either, art school can be terribly useful but it's not a must.
Some concept art key skills include:
Excellent illustration skills;
Effective communication skills;
Ability to visualise perspective and 3-dimensional space;
A keen interest in design, architecture and film;
Ability to visually interpret other people's ideas;
Ability to be flexible and to adapt to change when requested;
Ability to work as part of a team;
Knowledge of the requirements of the relevant Health and Safety legislation and procedures.
Some more info here.