After working in one industry for a while, you might find that it's a revolving cast of characters. People get hired and fired, and co-workers who once worked with one firm may eventually work for a competing company. If you have your sights set on working for a former colleague, it's not totally out of the question. But don't make the mistake of assuming your colleague will know why you'd make a great hire. Like any job, you have to be able to toot your own horn.
Conduct research on the former colleague's company so you'll be able to speak intelligently about its current projects and its modes of operations. Do an online search of the company to see what comes up. Check out newspaper reports and read the company website to learn about the company's products and services. Review the company's job postings to learn what the company values in its employees. From that research, decide which position you want to pursue.
Prepare your resume as you would for any other job. Use the information you've learned about the company to tailor your resume to the new job. For example, if the company has sought someone with organizational abilities for similar jobs, include details about organizational tasks you've handled in your past jobs. Consider adding an "Objective" section to the top your resume, which details the job you want and a few details about the skills or qualifications you have that make you a good candidate.
Prepare a few talking points to explain why you want to work with the company in question. Your research should have brought up some details about the company that you find intriguing or practical. It should have also given you some ideas about how you'd fit into the company. Jot down a few notes so you'll be prepared for a productive conversation. If you've been given special awards or had significant accomplishments in your past jobs, you should have mentioned them in your resume, but be prepared to talk about them. Your colleague may have some idea of what you've done in the past, but she's not likely to be following your career so closely that she'll know all of the details.
Ask your colleague for a one-on-one meeting. Treat her to morning coffee or lunch, and then bring up the prospect of working with her company. Give her a few copies of your resume and then explain why you'd be a great fit for the company. Hopefully she'll express enthusiasm for the idea right away. Tell her you'll contact her via email in a few days to check in. Try not to sound desperate. Like every other job candidate, you have to show you're worth hiring and you're not looking for special favors that will put you in a job for which you're not qualified.
Show your gratitude to the colleague for allowing you to make your case. Send an email or a hand-written note thanking your former colleague for the opportunity to talk about the openings at her company.
If the colleague is the decision-maker in the company, she'll be able to give you an answer herself. If she's not, ask her to put in a good word for you with the hiring managers. Also, ask her if you can include her as a reference for future job openings at the company.