This is going to be very basic because I want you to be able to understand generally how this works.
You should always assume that you are being monitored at work. Most times though it's just internet and mail traffic because it's easier and less stressful on the network. In order for this to be possible the traffic within the network has to be unencrypted, and is usually encrypted when you attempt to access anything outside the network (like google.com) through a forward proxy. Where your monitoring comes into play is when a transparent proxy is being used; which often acts as, or with, the router. Anything internal comes to the router, is reviewed, and is sent to it's destination.
So basically here is what happens:
You -> request connect google.com -> (switch if present ->) router -> proxy -> ISP -> internet -> google.com
@router - log created
@proxy - Check allow list (block/allow)
Now the proxy processes might all be lumped into the same location (such as the router) and works nearly simultaneously.
The very first thing you want to check is if you can use HTTPS. If you can, you can get around the proxy filter that might have black listed any websites. This is because your requests are no longer in plain text and do not tick anything listed on the blacklist. Logs created of this information will show gibberish. However, if the admin is at all competent this will be blocked. This can be done two ways; proxy denies any encrypted traffic internally from the network, or enabling https is blocked on your local machine. That is something you will want to check for. If it is local, there is a very good chance that your local machine is not being monitored at all times, and allows you to pentest a little bit without having to worry about getting fired immediately.
I'll stop here and let you ask any questions and others to comment before moving on. I don't want to overwhelm you as this can break into a very large discussion topic.
"The quieter you become, the more you are able to hear..."
"Drink all the booze, hack all the things."