PhD students can take a holiday or work from home whenever their advisor allows it I guess, but during undergraduate holidays you just keep working. I visited Royal Holloway this summer for a conference and the local grad students were still doing local grad student stuff. Have fun in the Happy Man or that medicin bar from time to time!

You are not the only one with this problem. My undergrad presentations where a hell and I could spend (more than) an entire semester pining about them. It got better in my first master years, but I would still be way too nervous and scared.

Then I started my PhD and a lecturer retired just before the start of the semester. Somehow I ended up giving one of his master courses. This was actually decided 5 days after the start of the course, so i had 1 day to prepare myself for a 2 hour theoretical lecture! I learned something about students that day: they know virtually nothing about your area of expertise. Teaching is a lot less stressful than presentations with professors, conferences and such. Some tips that are more specific to teaching:

* Know the topic: if you know it, you can talk about it for hours...
* Know your slides: mentally attach to each slide a part of the topic.
* Prepare some examples: students are not experts, you need to make the abstract more concrete.
* Prepare 2 jokes: A joke relaxes everyone and mostly yourself. I try to find 2 in case I forget one or skip some slides.
* Move around: You will be nervous (at first) but moving around is relaxing and makes everything seem more natural.
* Move around some more: To get really comfortable, you should be able to move around the entire room. Do something crazy like going to the door at the other side, looking outside and telling some random students to be quiet; or start messing with the shades on a sunny day; Look over the shoulders of a random student sitting in the middle row and comment on his notes/exercise. The main point is, it is your class and you can get away with walking around and not saying anything (important) for a minute.
* Dress well: I was 1-3 years older than the students in my class, dressing one 'level' above them helped in establishing a student-teacher relation.
* Be interactive: Ask a question and solicit questions from time to time. It is a bit relaxing as you can focus on the question instead of going on talking for 2 hours. It also improves the classes for the students and you can gauge their understanding a bit and adjust where necessary.
* There will be errors: You will make mistakes, your slides/exercises will contain errors and the textbook the students buy that has been used at many universities for years will still contain errors. It's my second year of teaching and this year I have found all 3 kinds of errors I just described. This may seem scary, but it is liberating to know that not a single student noticed them the previous year... As long as you strive to improve yourself, making errors is acceptable and usually goes by unnoticed.