As for the how and where, coming at this from the reverse side of things, when I started focusing on scoring, I put some flyers up at the local film school (here in Pittsburgh). I hooked up with a team for the 48 hour film project to refine my skills (this will be my third year doing it) and did as many student films and small projects that contacted me. An actor on one of those projects was editing another film, and he liked my work so he called me, leading to my first full-length. As far as time, it took me about 3 months to do over an hour of score and two 5-minute songs (though I was given little-to-no direction, tempscore or supervision other than getting approval for drafts). I'm sure future projects will be faster (and I do work a full-time job, so a full-time composer will be a little faster than that).
As far as costs, that's usually VERY negotiable. Many composers like myself are starting out and will work for peanuts (and portfolio pieces!) but good music is a LOT of work. Like anything else in life, find good people and treat them as well as you can. If I feel Director A is taking advantage of me, I won't be encouraged to work with them again. But if director B is paying me much less but treating me much better, I'll want to work on future projects, with the knowledge that if there IS money to be had in the end product, they will do well by me and send some my way.