The quickest answer is, stick to the nine typefaces considered 'safe' for body text, as described on this page:
You can expand that list a bit, if you understand the CSS 'font-family' rules, by using the Mac- or PC-only fonts listed on this page:
The second site is a bit erroneous when it comes to fonts on the first list, like Georgia, which is listed as PC-only. However, due to the nature of things, most Macs with popular web browsers will also have it.
Georgia, Trebuchet, Verdana and (I think) Courier New have the benefit of being more "screen readable" than the rest, even at the largest and smallest pixel sizes.
For headings <h#>, many web designers often choose fonts they don't expect many users to have. This is accomplished using Photoshop or another image editor's 'text' tool to work with the desired font from your personal machine and save it as a graphic (typically transparent) which can be viewed by most everybody, even with drop shadows or other nifty effects.
Sometimes, a designer wants to create a small image with very small text in it, like buttons or icons. In this case, or others where the number of pixels is known, we turn to a special breed of web fonts called 'pixel fonts':
While the general rule of thumb for web development at this time is to avoid 'user-downloadable' fonts, there is a notable exception. Scalable Inman Flash Replacement, or SIFR, allows headings to be dynamically generated. The browser's Flash plugin replaces the desired text with a graphical representation.
Browsers without Flash see the same text, rendered in the font as listed in the font-family CSS rule. With an eye to the future, the next likely standard for embedding fonts in a web document will likely be SVG (Scalable Vector Graphics) fonts, an XML technology.
Eric J. Bowman, principal
Bison Systems Corporation coming soon: a new sig!
I'm just a poor, unfrozen caveman Webmaster. Your new 'standards' frighten, and confuse me...