Be honest. Explain to your users how the money will be used and why you want to ask for it. It may help to explain why you are choosing to support the site via donations instead of other channels, like merchandise, affiliate programs, and so on. You might want to take the ads off the site, or at least explain how much money the ads make for you. Users often have distaste for paying for something and seeing ads.
Build a connection. Talk about yourself and your passion for the site. Why do you do this? How much of your personal time do you spend? Don't make it a sob story, but consider what you might say to someone if you were asking in person for their financial support.
Use a reputable channel to collect the money. PayPal springs to mind as a relatively easy service to use, both for you and your donors.
Consider putting a tasteful badge or link on most pages, then linking that to a separate page that has any explanations and a clear, call-to-action Donate link or button. While this adds a step to the process, I believe the good will you generate by pausing to explain what's going on and what will happen next ("When you click the Donate button below, you will go to the PayPal site.") will more than make up for anyone losing patience with the extra step.
Good luck! I love how your site is a reflection of your passion.