In Firefox, starting with version 2.0 spell checking is built in and enabled by default. Type something incorrectly and watch the red line appear underneath it. In some cases, you might have to right-click in the text field and choose "Spell check this field" from the menu.
To enable spell checking in Internet Explorer, you have to take an extra step and first download a free plug-in that performs the spell checking for you.
Once installed, you can right-click on text fields in your web browser window and select "Check Spelling".