When I started transitioning, I came out to all my teachers in person. Like you, I was in a small program, where I will likely have the same teachers and will be with the same classmates. I just asked to see them during their office hours, and would go and talk to them. Usually it was just a brief, "Hey, I would like to go by a different name because I'm transgender and am starting transition." And they were all fine with it.
I still have to come out to new teachers, because I've been on testosterone for a while and pass as male, but I'm in the middle of trying to get my name legally changed, so I still legally have to go by my female name on official university documents. Just a few days ago, I started a class and the teacher was calling the roll and when he got to my female name and I indicated it was me, he was confused and thought I was the guy on the roll before me, who was absent. I had to explain to him after class that I would prefer he not call my female name on the roll and to instead call me my male name.
As for classmates, I asked the teachers to change my name halfway through our first year together, but didn't really tell any of my classmates what was going on. I let them figure it out themselves. Anyone who was still confused probably figured it out when I came back last September after starting T just as school was ending last April, and I was passing as male. My classmates were great, they call me my male name, and say 'hey man', and stuff. If anyone has a problem with it, they just avoid me and that's fine.