As a missionary kid from Japan whose parents are still ministering over there, I'd like to share with any readers some specific ways to help and pray for Japan.
Ministry in Japan: Disaster opens up opportunities for the Gospel and compassion. One missionary, a friend of my family since the early 80s, is planning to load up on relief supplies and Gospel tracts and head down to the Sendai area. In addition, I can only imagine the witnessing opportunities that may spring up as people grapple with the questions of life, suffering, disaster, and eternity.
I trust that any who were planning trips to Japan specifically for the sake of ministry will continue with the plans despite what has happened; while the dangers are real, so are the opportunities and Japan now than ever needs willing Christains to come along side and both live and proclaim the Gospel. I am grateful that I know of at least one ministry, a camping ministry, which is going through with its plans to visit and work in Japan, despite the disaster.
In addition, financial aid is always needed. The Red Cross, of course, seems to be relatively quick to respond to disasters (http://www.redcross.org). My parents' mission board, Baptist World Mission, has also been organizing its own relief effort (http://www.baptistworldmission.org/component/content/article/1266-japan-earthquake-relief-effort.html) Although giving should never be viewed as an opportunity for "getting off the hook" as far as mission work goes (i.e. we still have an obligation to get our lives, not just our wallets, involved in missions), nevertheless we know from Philippians 4:15-18 that giving in of itself may be considered a ministry, especially when it is done sacrificially.
Prayer for Japan: 1. First of all, pray that the Gospel may gain a foothold. As I was flying home the other day, the man in a chair in front of me was reading a paper where the headline ran something like "In time of distress, Japanese rely on traditional beliefs," a headline flanked by a picture of a Buddhist temple. This naturally leads us to think of 1 Peter 1:18, "your empty way of life inherited from your ancestors" (NET). Japan has always placed a heavy emphasis on tradition, and Christianity has been viewed with suspicion as a "foreign religion" (never mind that technically Buddhism would also be a "foreign religion"). Nevertheless the Spirit possesses the power to make inroads into the heart with the news of Christ's death and resurrection.
2. Secondly, prayer is needed for the survivors, both those that are safe but lacking many of the basic conveniences of modern life, and those that may still be awaiting rescue. Continued safety should also be prayed for, as the potential for nuclear meltdown looms ominously on the horizon.
3. Thirdly, pray for those involved in the rescue effort, especially the JSDF (the Japan Self-Defense Force). One of my Japanese friends from my high school days, "Toshi," is in the JSDF and has currently been deployed to the Sendai area. I pray that the Lord will grant the JSDF both courage and safety as they seek to help those in need.