How do you motivate yourself to begin?
I think @"CW-Write Like You're Running Out Of Time" has a good point about not being afraid to write garbage, but especially with my first draft. Your first draft is not going to be good, so instead of focussing on writing the perfect draft just focus on getting your story onto a word document. I'm getting close to finishing my first draft of one of my stories, and I already know that there's certain parts that I'm going to need to edit like crazy.
For me, NaNoWriMo was really helpful in helping me getting started. Having a word count goal to work towards definitely helped me get going on my story and also helped to keep me going.
How do you stay motivated?
Set a goal for yourself. Sometimes that's a word count goal. Sometimes it's "I really can't wait to write this specific scene, but I'm never going to get there if I don't ever work on my story." Sometimes it's "I'm going to finish this chapter by the end of the week."
I also find that outlining my story is also helpful. I don't always stick to it, but it's just easy for me to get distracted when I don't know which direction I want my story to go. Having it all laid out makes it easier for me to stay on track.
Another thing is just to do some character or worldbuilding exercises. I find that drawing my characters or even just filling out pages on this site kind of helps me to stay excited and motivated about my projects.
Am I overthinking this?
Maybe a little :P Just start writing and edit later.