StbGuy is right if you'd like to talk in person. Opening up with "Do you have some time right now? There is something I'd like to talk to you about" is a great intro into it. And then you can start talking about how you feel. Maybe something along the lines of "I've been feeling really down recently and it's been getting overwhelming as of late" and then just describe your feelings and etc. Your teacher should be able to guide the conversation from there but definitely don't be afraid to ask if he knows any resources for depression that you could use.

I recommend talking in person but it's also alright to email the teacher first asking to set up a time. You don't have to go into detail but setting up a time that way may give you and the teacher a bit more time to prepare. People really do want to help so please feel free to lean on them for support. It's scary but the weight it can lift from your shoulders is most definitely worth it!

As for your friends, they may be generally good people but that doesn't mean you have to tell them. To be honest I'm not quite sure how many of my friends would understand it either. It's your personal problem so you can choose who to tell. Don't feel obligated.