To set this up, go to the Settings Menu (the gear icon on the top right), then go to Settings (yes - that's Settings in Settings).
Then go to the Filters tab to have Gmail (filter and) label for your incoming email. Click on the Create New Filter link and fill in the From box with the email of the person(s) that you want to label (my prof's, in my case - I created a separate label for each one to keep things straight).
If you want to test it, you can hit the magnifying glass button, otherwise just click Create filter with this search >>:
This will open the New Label box. Enter a new label name - I chose "Test" - and pick a place where in the menu you would like to have the labelled emails appear. I chose to put them under Priority:
Click [Create] to close this box and create the label.
Also - I chose to Star it and Always mark it as important. That way when a message came in about a class, it was collected into one place by the filter, and it is starred and marked important so that I could un-star it when I'd read it, and un-important it if it no longer applied - for example, if an assignment had been turned in or if the email was a class announcement like a upcoming event that the department wanted the instructors to promote. I did both of these because sometimes I could click on an email on my phone and just skim it or otherwise not actually read it and then forget about it by the time I got somewhere that I could do something about it. But that's just me.
What ever else you want to check, make sure you have the Apply the label checkbox ticked.
Don't wait until the messages start coming in - it will only process incoming email. If you already have email from the person (or persons) that you're creating a filter for, Gmail won't label them if they're already in your Inbox. If you wish to label already received email, you can drag them from your Inbox to your label on the left pane of your window:
One more thing- If you want to get rid of a label, hover over your label in the left navigation pane in your window, click the dropdown arrow and choose "Remove label". When you do this, it changes the filter that you created - it removes the label option, but doesn't change anything else. For example, if you set up a filter to label, star, and mark as important; then remove the label, it will still star and mark incoming email - it just won't label it because you remove the label it was using. Do do that, you have to go back to the Filters menu and delete it there.