Hello all. I’m looking for anonymous browsing for Firefox. Not giving away my true IP to any server. Can someone show me the basics? Thanks
Have a read of this first
https://support.mozilla.org/en-US/search?esab=a&product=firefox&q=anonymous+browsing
Aren’t those explanations showing how to not store anything about what you did on your own systm (cookies, history, etc.)? IMHO the OP asks how he can fool the server side in not knowing what the IP address of his client (his computer) is. I think using a proxy may help, but if that is sufficient?
Use a proxy. Or TOR.
Well, proxy or even VPN provider I guess…
If you are looking to browse anonymously without servers or third party sites / apps knowing your location, activities etc., then I suggest you go through this excellent guide which covers all the possible ways you can do it on a browser of your choice. Firefox, chrome etc.,
I suggest you also take a look at TOR guide - a browser entirely built from scratch for the sole purpose of browsing anonymously. However it is somewhat advanced and can be overwhelming at first. But after few days you will forget using other browsers 
Hope it helps
Have a look at https://panopticlick.eff.org/.
With Tor installed, your identifiability will drop considerably - we were trying this out at our local Linux Group yesterday.
+1 Tor browser bundle
https://www.torproject.org/download/download-easy.html.en
Simple to setup, works everywhere without any installation. In other words, no matter your platform, just d/l and run the browser bundle, do <not> install anything additional on your machine.
It accomplishes almost everything you want to do to protect your identify by default. Any modifications you make the default can decrease its effectiveness.
Be aware though like every other solution I know (including VPNs) is that your DNS queries are still typically in plain text and fully identify yourself… So, can be captured and used to analyze your activity. If you want to guard against that, requires an additional solution.
TSU
One additional solution which I think is referred to in this NSA paper: http://www.theguardian.com/world/interactive/2013/oct/04/tor-stinks-nsa-presentation-document is to open and close Tor only when you have had another connection open to the Internet for some time. This makes it more difficult for the spooks to detect the start and finish of a Tor session which is when they are most likely to be able to collect information about it.
Note that the weaknesses which NSA were able to exploit to some extent have now been closed by the Tor project - one reason for downloading it only from the Tor Project site.
We are almost three days into this thread, but the OP has never posted back.
Are we all dropping in our suggestions to no avail?
Maybe the NSA has caught up with the OP 
Quite possible. And those that advised TOR above are next. lol!
it is worth mentioning that using Tor is worthless if you enable java/javascript (a newbie mistake) as the ip address can be queried directly from the server providing the webpage. Also, there has been no mention of the Torora project which is also a viable alternative AND patches JRE to remove the javascript vunerabilty.
once you get knee-deep in this subject, you find that there are other subtle ways that you can be tracked by fingerprinting, I have difficulty keeping up with all the ramifications… 
Thanks to all. It’s a lot to take in. I’ll post again, once I sort through it.