Look at the mirror. Open your eye with your hand. (Make sure hands are washed). Place contact on finger. Slowly attach contact into eye. WAIT! dont close yet. Look down, then look to the left, then to the right, then look up and close. TADAH! Your contact is now in and feelin good.
I've been wearing contacts for over 20 years now. That's pretty much what I do.
Another tip, after you wash your hands, don't dry them. It will make the contacts stick a bit to your finger.
I'm told I do my kind of weird... I don't hold BOTH eyelids (top and bottom) open.
I'm right handed, so I put the contact on my right index finger, then (after making sure it's not inside out), I put a drop of solution in it. I've found that helps a lot.
Using my left index finger, I pull the lower eyelid down and look "up". (if you lower your head some, looking up means your looking into the mirror).
(by pulling on the lower eye lid, I mean like a child does when they place their fingers on their lower eyelids and "pull down" to make a scary face)
Then I place the contact onto the eye. Now, what makes people think that's strange, is then i "lift" the top eyelid up and "look down and then up". This caused the contact to align over the pupil. I then "let go" of the top eyelid and, like mentioned previously, move the eye back and forth/up and down to make sure it's all in place.
Sounds really strange does it not? Why do I do it like that? Well, I figured out on my own, that if you pull the lower eyelid down (instead of trying to hold both eye lids open), you CAN'T blink. Try it.