Have a look at the logos for existing meda institutions. Look at MAJOR and INDIE studios. (Hint; we're probably more indie than major!) Consider the MEDIA LANGUAGE - what does the design, the iconography, the font, the palette and so on communicate andout the institution?
Start sketching out your ideaS. (Creative people tend to have more than one idea!) Use a pencil or a graphics tablet. Check ideas with other people, including your teacher. Let them help you choose the best one.
Choose your tools
We would normally use Illustrator for this kind of design work. (You can use Photoshop too.) If you want to animate it, you need to have Apple Motion or Adobe After Effects. If youw ant to make a musical soundtrack to accompany it, consider Apple's Garageband.
Find a tutorial
The quickest way to learn to make a logo is to make a logo. And the quickest way to do that is to work through a tutorial. Here are a couple; one for a text-based logo, one for an image-based one. I'll throw in an After Effects tutorial also for the more masochistic/ ambitious students out there.