http://www.lmgtfy.com/?q=line+producer

As for the first part of your question, it takes time, patience and determination. While creative people pursue creative tasks (writing, directing, cinematography, etc), accountants and finance-oriented people (i.e. those without artistic talents) can pursue the career of a line producer. You'll most likely need to begin from the bottom (PA), then slowly work your way up. After some years, if you take some courses regarding budgeting (especially, film budgeting), network hard (and work even harder), you may eventually get a chance to put together a budget and schedule a shoot for a production.

I'm not quite sure that your question is really going to be answered all that well on a filmmaking forum. Most people that come here have artistic aspirations and would like to work in some of the "above-the-line" functions in the industry. Line producers deal mainly with the "below-the-line" crew, and those rarely visit filmmaking forums (unless they harbour secret artistic desires).

I hope to make this forum a place where new people feel welcome to ask
questions - even obvious ones. I think a filmmaking forum is a great place
to ask questions like this. Sometimes just using Google isn't the only
method. Sometimes making that personal connection can really make a
difference.

awantabee, the job of line producer is a difficult one. The line producer is
involved with budgeting and scheduling the film, hiring crew and making
deals for equipment so they need to really understand the nuts and bolts
of the process. Often it's a credit given to a Production Manager who has
gone above and beyond. Those two jobs overlap.

The path to line producer is usually PA>third assistant director>second
second AD>second AD> first AD> production manager>line producer.

Welcome to filmmaking.net!

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The aim of an argument or discussion should not be victory, but progress.
Joseph Joubert, essayist (1754-1824)