I recently won a scholarship related to my career focus. I was chosen as a winner in part because of a recommendation from a former professor. She is now asking me to draft a press release about winning the scholarship. I am hesitant because I do not want to appear press-hungry, but I would like to allow a write-up to be used as a means of increasing the visibility of the college and this professor. I do not want the focus to be on myself and my accomplishments. How should I handle this?
First, look at previous press releases from your institution and department. This may give you ideas.
But use the press release as an opportunity to speak to the public about things you deserve to be publicized. You're right, it doesn't have to be about you, but getting the fellowship is the award that gives you an opportunity to speak up about things you care. Press releases often contain quotes. In this case these could be quotes of other people talking about your involvement in a program you helped launch, or a quote of yourself praising whatever it is you want to praise.
In short: use that opportunity to promote something you believe in, in addition to pro outing yourself!
I do not want the focus to be on myself and my accomplishments.
While many of us (hopefully) have a modicum of modesty, there will be many times in your career where it is in your best interest to triumph your accomplishments, and this is one of them. In this case, it is a no-brainer: your former professor asked you explicitly to write the press release, and you should do it. Your university home page or newspaper probably has a news section that demonstrates the type of press release you're talking about (e.g., a short story with a picture and a description of the research and/or accomplishments).
The press release will be primarily about you (if you are the only winner at your school), but you should also include a paragraph about the scholarship itself and about the college and how it relates to the scholarship (e.g., "The X Scholarship has been awarded at Y College for the past 10 years, and was funded through the generous donation of so-and-so, who graduated from the college in 1954...). If it fits in, you can mention your professor's relationship to the scholarship and your involvement (how did she know to recommend you? Was it her impetus or yours?).
If you're concerned about how to write the press-release, I would reach out to someone with journalism experience, whether it is someone who works for the school paper, or the news-section of the school website.