You can clear all privacy related settings via the clear private data button in the preferences. This will clear browsing history, cookies, etc.

If you need specific control over what is cleared the two following addons can tweak the behavior.

https://addons.mozilla.org/en-US/mobile/addon/cleary/

https://addons.mozilla.org/en-US/mobile/addon/clear-mobile-history/

I have installed both of these add ons and still can not delete my history fill or the ALL files!

If you are having trouble clearing Firefox's settings in the application then you can use the system wide settings. This will reset Firefox to a base install.

• press the Home button
• press the Menu button
• select Settings
• select Applications
• select Manage Applicaitons
• select All
• select Firefox or Firefox Beta
• select Clear Data

For selectively deleting history particularly after sorting on a column or after a search, see

• http://kb.mozillazine.org/Viewing_the_browsing_history_-_Firefox#Selecting_history_items

dmcritchie this is a mobile support question your answer does not apply.

Oh, oh, sorry, and a bit uncomfortable that mobile version would be different. I'll be wary of Android and of "mobile" tags until I have one.