For those new to TextMate or just not intimately familiar with it yet, Soryu has written a setup tutorial which walks you through the steps of setting up your preferred tab size, theme (colors), installing the
mate shell command, and gives a few details along the way, such as the fact that TextMate’s spell check as you type only will spell check your prose (and ignore keywords or markup.)
There is also a thorough basics tutorial which touches bundles (snippets, commands, etc.), various editing modes and actions, navigation, common bundles, and similar.
Since there is a lot of information to devour, David Powers has created a succinct cheat sheet (direct link to PDF) which you can print and have next to your computer. It lists key equivalents for many useful general actions.
For less language neutral cheat sheets, you can google for TextMate cheat sheets (PDF). I have previously mentioned the Rails cheat sheet and there is also one more targeted for HTML/CSS/PHP (PDF) developers (I found this from the Google search, so I do not know to whom the credit should go.)