Hi Lukas, you and I are in similar boats. I too live far away from my parents, but will be staying with them this summer and plan to come out to them while I'm staying there, I feel like person-to-person is best for the relationship we have. I plan on just saying it to my dad, but will be writing a letter to my mom. My gender counselor has suggested I keep it reasonably short, since with surprising news people can usually only grasp a few new concepts at a time. I plan to write out several things:
1. I identify as a male, not a female. I prefer the masculine pronouns of he/him. (She may or may not have seen this coming. I'm already "gender deviant" [not her words] and people have been confusing me for her son in front of her for a LONG time)
2. I have been seeing a gender specialist for 7 months who thinks I am of sound mind and am making a good, healthy decision.
3. I have already told this to my friends, colleagues, and some members of our extended family, and have been accepted. In fact, most people have not even batted an eye. (I feel like this might help relieve some of her stress, since a main concern of hers is my success and safety)
4. Not much is really going to change. I'm still on track to getting my advanced degree, I'm still going to pass the board exams, I'm still going to get into my career, get married, and have children.
I don't plan on using the word transgender in the letter, it's not really necessary and may be more confusing/stressful at the beginning. I do plan on having some reference reading material that will certainly have that in there, though. I also plan on having somewhere else to stay for a couple of days just in case things get too awkward in the house while it's sinking in.
Christopher has a good outline for questions, and I'd like to second his suggestion of making sure you don't come off as apologetic.
Emphasize that you aren't really changing that much, and that everything is going to work out for the best.
If she likes documents and things to read, I highly suggest considering additional reading material for her. PFLAG and Tranifesto both have material for parents of Transgendered children/adult children available for free or for not much.
Good luck!