I plan to use a DNS service, I'm just wondering what sort of information gets sent. Will my passwords, browsing activity flow through the DNS servers? I kind of know what a DNS is, but I'm not sure about the security risks from my point of view, I don't want my passwords compromised.
A good way may be to learn how DNS works. When you connect to a machine, you actually connect to its IP address (say, 18.104.22.168). Instead of you remembering all these numbers, DNS facilitates translating names (such as google.com) to these IP addresses.
A "normal" DNS query is, is basically:
"What's the IP address for www.google.com?"
Its response is
"The IP is 22.214.171.124".
So, in short - and under normal circumstances - no, they won't see your passwords, but yes, they will see your DNS traffic (and hence, figure out what websites you visit and services that you use).
However: a rogue DNS administrator can forward you to the wrong server. Instead of accessing server1.com (which is at 126.96.36.199), the malicious response will say that it's at 188.8.131.52, a server controller by an attacker. This malicious machine has the exact same look and feel as the original server, so it may (SSL errors aside) look normal to you. You, as an unknowing user, will just log in using your credentials. They can see these credentials, and hijack your account. So, in short - yes, DNS is a dangerous service that is often blindly trusted.
Why not use OpenDNS or google's DNS servers?
You're using a DNS if you can access "www.Google.com".
DNS converts that human-readable name to the machine-readable IP address of the website (in Google's case, to this for example:
http://184.108.40.206/ (< copy and paste in your address bar, and you'll access Google.com)
Only addresses are sent through DNS servers NOT your passwords/data.
Google Public DNS: 220.127.116.11 and 18.104.22.168