When you compose email messages from Hotmail, you will not be able to tell if the grammar and spelling of your message is correct; this is a feature to keep in mind if you are accustomed to writing content in advanced text editors and word processors like Microsoft Word, which will be run the spellchecker "on-the-fly", and add wavy underlines where it thinks you made a mistake (in Word, redirect waves indicate spelling mistakes, blue waves for formatting issues, and green wavy underline means grammatical errors - the screenshot below is taken from Word 2010). But Windows Live Hotmail comes with a built-in spell-checker, which you can run manually - on demand. Unlike some email programs like Microsoft Outlook, the Windows Live team has not yet added settings like "Prevent me from sending messages with spelling errors", which means that you'll need to remember to manually check every email before you send it.
When you are inside the email composer window, type the body of your message as you usually would; when you are done with the entire content, or a portion of it worth proofing, click on the "Spell check" button /link in the toolbar, above the editor: (it shows "Identify possible misspellings (F7)" as tooltip when you hover above it).
Tip: Hotmail also support the same keyboard shortcut found in Microsoft Word and other Office applications. Press the F7 key to check the spelling of the message you are editing!
At this point, the Windows Live spellchecker doesn't include corrections for grammatical mistakes, so you'll need to resort to external options to cope with this lack; these relatively time-consuming alternatives make it worth only for important messages, like tending your resignation or asking for a raise.
Compose your email message inside Microsoft Word or an advanced word processing equivalent - note that the "Word Web App", which allows you to create and edit Office documents from Hotmail, doesn't yet support grammar checks - but unlike the email editor, it does support "on-the-fly" spell checking.
A second option is to use a free online grammar checker of your choice. In our experience, these fall quite dramatically short - some of the paid online grammar check tools are better, and we'll post soon a link to one of them.