As Ian said, you will have to make sure that SSL Enabled is set in both the site settings (Admin > Site Settings) as well as the specific Page Settings (Settings Icon in the control panel or via the Admin > Pages for the page(s) you want to secure. You may also want to watch out for the Enforce SSL option, as it will prohibit access to the page using the https protocol.
Regarding the Untrusted Certificate error, much as David also said, if you plan to put your site public you will want/need to get a SSL from one of the trusted providers. I personally use GoDaddy for my SSL Cert purchases, and they are run through Starfield Technologies. I think we pay ~$35 (?) per year for a 'basic' cert.
Just a quick note - I ONLY use GoDaddy for SSL purchases and Domain registration / management (I handle ~300 domains for various clients). Their phone help (stubborn inbound transfers usually) is usually spot-on. However, I handle all hosting in-house. I have heard some real horror stories about hosting DNN on GoDaddy, especially if you don't pony up for a dedicated server - the only option they have (last I checked) for getting Host-level access or having DNN 5.x installed.