Along with Ferodynamics' suggestions, you could also do the following:
- Charge some members for a premium membership (e.g. most deviantArt users don't pay a cent and have access to most features; but a small minority choose to pay for a premium membership that gives them access to additional features).
- Sell branded merchandise (t-shirts, hats, mugs) or supplemental products (e.g. Wikipedia offers their entire database on DVDs; deviantArt users can sell prints of their artwork, with dA taking a small percentage of the proceeds).
- Find corporate sponsors—this is similar to asking for donations, except that you target large companies that want to give to charities for tax or PR benefits.
- Apply for grants—you can apply for grants offered by private companies, non-profit organizations, or the government.
Alternatively, some commercial companies (e.g. developers of open source software) offer products for free but gain free publicity and have their reputations boosted by the popularity of their products. They can then offer other commercial services which subsidize the development of their free products. For instance, CakeDC produces the open source MVC framework CakePHP. But they make their money from offering consulting, development, and training services related to CakePHP.
Likewise, if the educational platform you're using for the site can be re-purposed for enterprise e-learning or knowledge management, then you can license it to commercial companies to pay for the free website. Or, with an SaaS model, you can use business memberships to subsidize the free memberships offered to private users.
Christopher makes some good points about asking for donations. If you're only collecting relatively small amounts of money, you can easily set up a donate button from Paypal (if you're collecting a lot of money, you may consider subscribing to a payment gateway). Additionally, you should state what you'll be using the money for (e.g. hosting, hardware, new features/services, etc.) and perhaps offer recognition to those who donate. Some kind of fund-raising meter can also encourage donations and provide a sense of transparency/openness.