Here's a recent thread where we discuss what responsibilities a DP has, both in preproduction and during production: http://www.cinematog...291#entry429058
It's by no means a complete list, but you might find it helpful. Simply put, it's your job to fully understand what visual style the director wants for the project and then figure out how to deliver that with the time and resources that are available to you. So your first step would be to read and understand the script fully, try to imagine how you would make it look, and what if any technical or artistic problems or challenges that approach would present.
(Some DP's say they don't like to do this before they speak to the director in case they have a completely different vision from yours. But I always like to be prepared with an alternative in case the director doesn't have any strong ideas, or has an idea that I don't think works, or is unrealistic. I feel like it's part of my job to be ready with lots of creative options.)
Next, have a meeting with the director and try to figure out what approach they want. If they bring up references like 'Breaking Bad', watch them carefully for visual style: locations, lighting, color palette, lens selection, placement of camera and camera movement, editing. There should be some obvious link between the two projects - maybe your assignment takes place in a run-down suburban house or has a big day exterior scene in a desert like 'BB'? Maybe your story is about a quietly desperate middle-aged man who flips out? What is it about the style or mood of 'BB' that the director wants for your project? If you still can't figure it out, ask them.
Finally, once you feel like you are both on the same page you can start a full breakdown of the script scene-by-scene and figure out where and how to shoot it, what equipment and crew you think you will need, any special props or effects that may be required. You can now start having production meetings with the director, production designer or art director, 1st AD, and other department heads to make sure everyone is on the same page. Pay special attention to locations and sets, since you can't easily change them once they are locked in and will largely determine whether your shooting plan is doable and will look good.
I feel that most of the work of a DP is done in pre-pro, so once you get to the production phase things should be more about executing a plan than improvising solutions. Of course, there are inevitably problems that come up requiring improvisation but you will have a better chance at finding good solutions if you have an overall battle plan. And you will get much better at improvising with experience, so don't feel too bad if you make some blunders. It's all a learning experience.