How can I share a post on my wall using the Facebook app? On my PC, I can repost (share) a post from a friend on my own wall.

How can I do that in the official Android Facebook app?
You can re-share your friend's post using FriendCaster for Facebook app. Simply install it and use it as your primary fb app. Its better than official fb app in many aspects..

Update (November 2012):
In recent version of official Facebook app, this feature has been added. Happy Re-Sharing!