From DailyKOS:

Whatever happens with the Supreme Court nomination battle that is about to ensue, it's going to happen fast. Here are some things you can do right now:

• If you have a cell phone, sign up for People at the American Way's Mass Immediate Response site. This way, you'll be able to receive text message action items instantly as events break. (If you signed up during the nuclear option fight, you'll need to re-sign up.)
• Also sign up with the Save the Court, another PFAW website devoted specifically to this issue.
• Recruit friends and family members to the cause.
• Write to the President, telling him he should choose a consensus candidate to replace O'Connor.
• Contact your Senators to tell them the same thing.

Also: Write to your local newspapers. Make your views clear. We knew this fight would be coming, people. There's no reason to be surprised by it. Tell your friends and family why you are concerned. Organize local action. Write editorials. Apply some pressure.