You may want to check out the Training Techniques forum. Here is a thread I have in there explaining how I taught Ollie how to wave:
Video of Ollie waving. I use clicker training, which I find to be very effective.
Getting a bird to lay on its back in your hand is more of a trust issue than a trick. No matter how hard you try, if the bird isn't completely trusting of you then it's probably not going to happen. The way I have gotten Ollie to lay in my hand is by first teaching her 'to be a bat.' For some reason, whenever we go into the bathroom she will hang upside down on my hand to drink out of the sink, or chew on the hand towel. I would follow this with the cue word "bat." Once she learned that trick, I simply started putting her in my hand. It's taken quite awhile for her to feel comfortable enough for me to remove my fingers from her grasp. Sometimes she still won't let go.
Here's a video that explains the "bat" trick:
YouTube - Ollie's Trick Series