As the words begin to flow, the ideas will come out from the shadows and let themselves be captured on your notepad or your screen.
分析主干：the ideas will come out and let themselves be captured...
句首的as 引导时间状语从句。主句部分是复合谓语，有两个由and 连接的并列谓语。
译文：随着话语开始流淌，思想也会逐渐明朗化，使自己呈现在你的笔记本或者屏幕上。