The least-effort strategy, and the one I used for my current job, is to talk to recruiting firms. They have access to job openings that are not announced publically, and they have strong financial incentives to get you hired. The usual structure, at least for those I've worked with, is that the prospective employee pays nothing, while the employer pays some fraction of a year's salary for a successful hire, where success is defined by lasting longer than some duration.

(I've been involved in hiring at the company I work for, and most of the candidates fail the first interview on a question of comparable difficulty to fizzbuzz. I think the problem is that there are some unteachable intrinsic talents necessary for programming, and many people irrevocably commit to getting comp sci degrees before discovering that they can't be taught to program.)