Customizing home page

I’d like to have my home page be a static page that has a slightly different layout than the rest of my site. Specifically, I don’t want my home page to have sidebar type content on the side; I want it on the bottom. I’m guessing I should have two different templates: one that treats sidebar in the home page way and one that treats it for other pages.
Is that right? If so, how do I say “if this page is home page, do x. If not, do y”?

Thanks,
Adam