A judicial externship is a special opportunity to see how justice is administered. With the exception of post-grad clerkships, this is one opportunity many will not have again in practice. That said, you should consider what your goals are for the experience as it will help guide where you apply (both geographically and to what court), and if another experiential opportunity might better serve your larger career/ learning objectives.
What do you want your interactions with the judge or clerk to be like? Do you want more research or more court observation?
Apply early, and possibly late also. The timing of reviewing applications and conducting interviews varies greatly by location and judge but a majority of hiring for the Spring Semester takes place in September and October. If you don't have a placement by the end of October and are flexible about where you work, there will still be some positions available. With the exception of the new online system for the U.S. Northern District http://www.cand.uscourts.gov/externships, there is no easy way to tell if a judge/ court has openings and when they are conducting interviews. First check if the court has a posting on the UC Hastings site, or on the court's website. If not, it is acceptable to contact the court and ask if applications are being accepted for Spring 2017. Start by selecting five or so placements you would happily say "yes" to. If those don't work out, then move on to additional placements.
All chambers expect that you will submit a cover letter, a transcript (unofficial is fine), a resume, three references or letters of recommendation, and a 5-10 page writing sample. Some chambers have additional requirements, look for these in the posting or ask if there is anything additional when you contact chambers. If you are submitting via email, put all of the documents into a single pdf for the convenience of the court. As you know, proofread carefully, including your email note submitting your materials.For More Information or to Confirm Your Externship Contact Professor Brittany Glidden, email@example.com.