Let's start by checking that you're doing the correct thing anyway:
With only one tab open, go to google.co.uk. Then click on Tools > Options. If 'General' isn't already selected, click on it. Under 'Home page' click 'Use current pages'. Then (if you want your Start Page and your Home Page to be the same), change 'When Firefox starts' to 'Show my home page'. Click on 'OK'.
If you've done that and you still keep getting Yahoo then you've probably got a Yahoo toolbar (or similar Yahoo extension) installed. Go to Tools > Add-ons > Extensions to see if it's listed. If it is, click 'Remove'.
If none of that works, go to Tools > Add-ons > Extensions again to note down the names of any extensions that you want to keep (because you're about to remove them). Then go to Help > Troubleshooting Information and click on 'Reset Firefox', at the top right of the page. (Don't worry. You won't lose things like your bookmarks!). Then reinstall your extensions. Finally configure your home page, as per the instructions in my first paragraph.