While I can easily do tripod headstand with my knees on my elbows, the thought of reaching both legs into the air scares me. I also can do hardstand with my head in my hands and balance with legs against chest. I guess I am afraid of falling out and getting hurt. How did you overcome this?
Warning: NEVER TRY TO ATTEMPT THIS…!!!
For some advanced yogis, elephants seem to facilitate asana practice…!!! 
first practice headstand/handstand against wall to an extent that you can stand without touching wall though wall is there to prevent fall. Once you achieve this will confidence then read my post
http://www.yogaforums.com/forums/f16/handstands-11447.html
The larger question that comes to me on this is “who is your teacher and how are you working with that person to address the issue you’ve raised?”.
I agree with Inner athlete about the value of teachers in Yoga. Many times a teacher can see something you are doing wrong that you can never see by yourself. Or a teacher can give you advice on how to achieve a certain pose that you would never get on your own.
In the case of inversions of which you have a fear a teacher can be key in giving advice, encouragement, and confidence.
I myself never did a headstand til I hit the age of 63. On my own I could never do this I feel. But through daily classes in which a headstand was part of a flow I began to gain the insight and confidence i needed. And then one day it just happened. It was part of a process not a single event.
So on this forum we can give you our advice and experience, but the daily process and education through a good teacher in a class is a healthier wiser and safer way for the process to take place.
Standing on one’s head can be “achieved” by almost anyone. Doing Sirsasana (properly) requires guidance.
when I started out. just getting into the position was more important for me than staying on it. Once after getting into the position was no longer a problem. Staying in that pose took time but with time the fear of falling goes. and then having a wall support always helps.
I’m not a big fan of head stands or hand stands either, but I’m ok with a supported shoulder stand…. one of these days I will go back to a teacher and work on head stands and shoulder stands again but for right now I’m good.
Doing hand and headstands is like going down a ski slope. You have to let go and just do it. If you hold back, you will fall. But the snow is soft and the floor is not too far away.
Perhaps practicing falling first would make you more confident?