There are two main ways this can be accomplished -- the easy way and the hard way.  The easy way is simply connecting to a search engine that lets you search by IP address.  The hard way is to do DNS lookups on all the domains you can find (which can involve a huge database).

I've done it the hard way (www.DNStrails.com), and chose that way because it is the most reliable (I don't have to worry that Google or Bing is going to stop allowing queries), and fastest.

The only way to find out what domains are on a website are to somehow find those domains (you can get a list of all the domains on gTLDs; search engines find many more as well as subdomains on the pages they visit).  Occasionally, people will set up the reverse DNS for the IP of their server to have records for all websites the server handles, but that is rare.

The trust is based on the source of the information.  You can easily verify that the information displayed is correct (e.g. do a DNS lookup of the website to make sure it matches the IP you entered).  But what you do not know is what is not displayed to you (e.g. if there are domains that are hosted on the IP, but not shown; for example, subdomains or domains on ccTLDs).