You might find Didaskalos's blocking notation cheat sheet helpful (
http://smnetwork.org/forum/index.php/topic,1884.0.html).
Basic blocking is pretty easy, once you get the hang of following the script and watching the actors at the same time. The notation is up to you, as long as you can understand what you've written later. Some SMs like to draw pictures; I prefer to write it out in words unless there are a ton of people onstage. Whichever works for you is great!
I feel like it's easier to show a blocking script than to try to explain it, so I've attached a page from my Angels in America script. You can see that the numbers on the script side correspond to the actors' movements. I like to use odd numbers so that I can go back later and add in more blocking if I need to without having to change all the numbers. Figure out a system of abbreviations that will work for you so that you can write quickly and legibly.
Blocking for musicals can be a little trickier because of choreography. As the SM, you aren't responsible for writing down the specific choreography steps - instead, I usually just draw little pictures of where everyone is onstage, especially entrances and exits.
Finally, the best advice I can give you is to not worry if you miss something! The scenes will undoubtedly be rehearsed multiple times, and it's easy to fill in the gaps the second time around.
Good luck!