Forbes recently posted an article by me called "10 Secrets to Getting a Job at Apple, Google, or Microsoft." Here are three of my favorites:
Start Something: Launching a small tech company, or just a project, can demonstrate virtually everything a tech firm wants to see: field expertise, passion for technology, initiative, leadership and creativity. Don’t have software development experience? Not to worry – you can hire an outsourced development team from sites like odesk and elance
Create an Online Portfolio: Almost everyone can benefit from a portfolio. A simple web site with a description of your major accomplishments (both inside and outside of work) can provide more context than what your resume can provide. Recruiters may reference this after seeing your resume, but they might stumble across your portfolio online and give you a call.
Rehearse Your Stories: One of the best ways to improve your overall interview performance is to practice your “stories.” For each major accomplishment, brainstorm ways that you showed leadership, demonstrated influence, or overcame challenges. Rehearsing these responses aloud will help you to more effectively discuss what you did and why it mattered.
As an addendum to this, I'd like to add: ask for help. There are people in your field (or your desired field) who can help you. They can suggest ways to get relevant experience through projects, volunteer work, or starting a part-time job. They can help you craft your resume to bring out your best accomplishments. And they can help you prepare for the interviews. Don't do it alone - ask them for help.