If you have a newer phone with "applications" you can go to the "market" and download "applications" for free ringtones. Some applications allow you to download as many or as few ringtones as you wish.
There are a couple websites you might consider. Shop for phones and phone accessories on any official At&t or Nokia website. In addition you can visit your local electronics store.
Its pretty easy, all you need to do is search zedge in a search engine. When you find the site just type in cellphone brand and start downloading for free.
Its very simple. Go to a search engine and look up both of these free ringtone sites zedge and myxer. Zedge will let you download witout signup/myxer have to signup.