how do i connect a 2009 imac to a 2014 mac mini

An external display would be a better option for the 2014 Mac mini.

If you are set on trying to use the iMac as a display for the Mac mini, then both must meet the following requirements. carefully read > Use your iMac as a display with target display mode - Apple Support

Basically the iMac must be a Late 2009 27" iMac,

the 2014 Mac mini must be running Catalina or earlier,

plus you need to use a Mini DisplayPort to Mini DisplayPort cable.

see this link:

https://www.macworld.com/article/701548/how-to-use-file-sharing-mac.html

Why do you want to connect them? Share files? Use the iMac as a monitor? Please help us help you,