Not a basic question at all! And asking it in public helps increase awareness.
DuckDuckGo uses HTTPS which is a secure connection, so when you go to duckduckgo.com you should see https:// in the URL bar and a padlock icon. This creates a secure tunnel between you and DuckDuckGo - the ISP cannot see what you're searching for. However once you click on a link and a new website opens, a new connection is made. This could be insecure (HTTP) or secure (HTTPS):
* HTTP: The ISP knows which pages you're visiting and could see the data you send and receive (as can anyone else on your local network, e.g. in an internet cafe).
* HTTPS: The ISP knows which domain you've visited but not the URL parameters, and not the contents of any data you send or receive.
A couple of caveats:
1. If your search parameters are in the URL (e.g. ?q=example) then your search query will be in your browser history, even with HTTPS. If you don't want this, go to DuckDuckGo's menu -> Advanced Settings -> Privacy and turn "Requests shown in url" off.
2. It's possible for the ISP to perform a "man in the middle" (MITM) attack and intercept your HTTPS secure connection. This is unlikely but not impossible - see this thread for a good explanation:
Hope that helps.