For those who are apprehensive about going upside-down in a handstand, the headstand is a good skill to get you use to being inverted. It is a fairly simple skill that you should be able to master very shortly.

First, let's look at the head and hand placement for the skill -

What's important to note here is that the hands and head are NOT in a straight line. That's the mistake I see the most often. Instead of a straight line, you'll want to space your head and hands out so that they make a triangle. Your hands will be a little more than shoulder width apart and far enough away from your head that your arms will be bending at about a 90 degree angle (you'll see this clear in the pictures to come). Your bodyweight should be evenly distributed between your head and each hand. All this will give you better support and balance in the skill. Put a pillow down on the ground if you're practicing on a hard surface.

With this head and hand position, put one knee ON TOP of one of your elbows. If your arms are bent correctly, your knee should sit up there like it's on a shelf.

Bring your second knee up on top of your other elbow. This is a position know as the "tripod".
 

You should be very stable in this position - just like a tripod. If you feel like you're falling (especially to your back) then get down and reposition your head and hands to make a bigger triangle.

Here is a view of the tripod from the side. Notice how my knees rest on my elbows, and that my arms are bent at about 90 degrees.

When you feel comfortable with the tripod, start to lift your legs up.

And hopefully end in a headstand.

From here it's pretty easy to hold the position. If you have to put more weight on any part of your body while balancing, put it on your hands, as then can push and balance you better than your head can.

Here's the headstand from the side. Notice that my body is straight. There's no need or reason to arch, as you have three points of contact with the ground and plenty of balance.

Feel free to practice against a wall if you're worried about toppling over your head, but you'll soon be getting into a headstand anywhere.

I hope this helps people feel more comfortable when getting into a handstand. Good luck!