While there is no known way of automatically jumping to the first text field on a page if the option is not enabled at the website itself there is a way to make the procedure less complicated and mouse-less. Pressing tab will flip through the elements on a website. By default all elements – this includes links and forms – will be focused when pressing the tab key. There is however the possibility to alter that setting in the web browser’s options to only focus on text fields on the active website.

The setting can be changed in the about:config parameters of Firefox. To open these settings enter about:config in the Firefox address bar and hit enter. If this is the first time that you access the options you need to press the I’ll be careful button before to continue.

Filter for the setting accessibility.tabfocus.

Double-click the entry to change the parameter to one of the following:

• 7 – Default value. Jumps to any form and link element on the page.
• 1 – Will only jump to text fields.
• 2 – Will only jump to form elements other than text fields.
• 3 – Will jump to all form fields.
• 4 – Will only jump to links.

Changing the setting from 7 to 1 will have the desired effect. Pressing tab on any website will now focus the first text field on the website.

Update: There is a Greasemonkey script that can enable the behavior on specific websites automatically.