Android - How to turn off ringer when connected to particular wifi network

This isn't built-in functionality, but it's something you could achieve with a trigger/event app such as Tasker. This kind of app runs in the background, and lets you configure certain actions to take (such as turning off the ringer) when certain events occur (such as seeing a particular Wi-Fi network). Tasker's not the only such app, but it's very complete and has some users who contribute to this site, which means that if you have questions setting it up you can probably get them answered here. See tasker.

The Llama - Location Profiles application should help too. This application uses phone masts around you to determine your location and switch profiles.

Llama uses phone masts to determine your location, so that you can change your ringer, vibrate and ringtones depending on where you are as well as the time of day. Llama provides you with sound profiles so you can quickly switch between quiet, loud, silent and normal sound settings. You can set your family, wife and children to ring even if your phone is set to silent! You can create events and home screen shortcuts to manage your sound profiles and more:
-Silence your phone at work
-Turn your Bluetooth on ready to connect your headset for a morning run
-Set your phone quiet when it's late at night and you haven't gone out
-Start the music player when a headset is connected

I personally recommend AutomateIt. Not only can it achieve what you are wishing for, but it can also save you some battery life too. The app lets you scan surrounding cell towers in order to determine location. So in this manner you can silence your phone as soon as it connects to a nearby cell tower at your workplace. This way you save some juice by not having to keep your wifi on to determine location.

Give it a try, and if you love it enough, upgrade to the Pro version to make fancier rules that can better suit your needs.