If you want to be anonymous and are worried about geolocation, don't grant websites access to your location. You will be prompted about whether to allow a website to access your location before the website can use HTML5's geolocation feature to locate you; make sure you don't allow it.
More generally, follow all the standard strategies for surfing the web anonymously. For instance, use Tor, and use it properly. There's a lot already written on this topic on this site; use search to find it. See, e.g., Different strategies for online anonymity and their +/-s?, How to be completely anonymous online?, How much can I trust Tor?, What are the pros and cons of a VPN for privacy, How can I use a VPN to protect my privacy, How to browse the Internet safely?, Does Java applets reveal the real IP address, even when using proxy or vpn?, Improving the privacy of a casual Web user, Is it possible to Identify a VPN user by finding relations in traffic?.
While D.W. has provided an excellent answer, I'd like to go a step further with the possibility to falsify your true location.
Depending on the specific case it might be be better to provide a fake location rather than just withhold your true one. I can think of one use case:
A web service (might be a game) that is strict about duping (creating duplicate accounts) they utilize both IP and (might also force) Geolocation API checks.
† Here's a video that demonstrates how Geolocator works with Firefox.
Turning off geolocation functionality in your browser doesn't mean you browse the internet anonymously. The only thing it does it stops the browser from sending geolocation data to the server. The geodata may consists of your country name, city, street, gps coordinates (approximate). However the server still gets your IP address for example.
Using a single proxy server also doesn't guarantee you full anonymity because for example your IP address and your request datestamp are stored in the proxy server's log file.