Because response always comes as a result of something, some text that precedes it, which must be read and responded to, the process of writing a response actually begins with reading. Don't shortchange this part of the process because your success throughout the process will depend on your initial attentiveness to the text you are responding to.
One important thing to think about as you begin a response process is the assignment itself. What do you know about the audience and the purpose of the response you are about to write? What more do you need to find out?
A second thing to consider is the deadline for the assignment. Be clear in your own mind about due dates, and then backward plan from that due date to the current date. Divide up the tasks of the response, allowing yourself time to read, react, draft, collaborate, revise, and even seek a full-scale peer response or workshop opportunity.
Don't allow yourself to procrastinate simply because the task seems overwhelming; instead, chip away at it, a little bit at a time, and you may be surprised at how smoothly things go. Among other things, when you address the assignment early and give yourself time to think (and actually do that thinking instead of avoiding it) you actually end up incubating ideas even when you're not fully conscious that you are doing so. This mulling over of your response will tend to make the writing of the response go much more easily and should actually help you produce a better response because of your full engagement with the material. Starting early will help you filter out less good responses over the course of the assignment period.
Just as soon as your initial reading of the text has been accomplished, then critical thinking can begin, and this is perhaps the most essential component of your pre-writing efforts. A good place to start is with a double-entry journal.