You can't run browser games locally, so you need to upload your exported project to a web server of some kind. The Scirra Arcade, Kongregate, etc. are all capable of serving web pages, or you could take out a web hosting hosting with a service provider.
By far the easiest method, though, is with a Dropbox account. Download and install Dropbox, create a public folder within it (literally just a folder called "Public", copy your whole project folder there, right-click index.html and select "copy public link" and paste that link into your web browser. Dropbox acts as a limited web server and gets the job done for testing and simple sharing.