The way I usually like to start a manuscript for a children's picture book, after I have the basic idea in my head, is to just write it down on note paper with a pen. I like to double space it to leave lots of room for scribbling out and adding stuff between the lines. Then I'll just keep going over it and refining it until it gets to a point where I'll re-write it in a somewhat more neater fashion. Then it's off to Google Docs to begin writing on my computer where spell check is a blessing, I'm definately not a very good speller.
Lately I like to sit at the dining room table with my daughter to write my manuscript while she is writing in her journal (a dream journal right now, she has the most interesting dreams) or reading or something like that. I'll also have other picture books around for inspiration while I write or work on illustrations.