I hope you'll begin by seeing this as an opportunity God is giving you to serve Him by using the gifts He has given you. The Bible says, "We have different gifts, according to the grace given us. If a man's gift is.... leadership, let him govern diligently" (Romans 12:6,8).
In other words, don't see it as a burden (although I'm sure it won't always be easy), but as a blessing -- both for you, and for those you'll be helping. Assume that God has put you in this position, and that you have the support of those who elected you. Approach it with humility, knowing that you have much to learn -- but approach it also with courage, knowing that God is with you and can use you.
I suggest you begin by gaining as much wisdom as you can from other members of your church's board (including some who served in the past). Avoid focusing on issues the board may be facing; you don't want to take sides on issues until you have the full facts. Ask instead more general questions about the responsibilities of a board member. In addition, be sure you're acquainted with the church's bylaws or other rules concerning the board's responsibilities.
Most of all, commit this responsibility to God, and pray for His wisdom and grace in all you do. The Bible says, "If any of you lacks wisdom, he should ask God... and it will be given to him" (James 1:5).