Okay, here's how I usually put them in. I forget whether you're right- or left-handed, but if left, you should reverse hands, obviously.

Put the lens on your right index finger, with the center of the convex side resting on the tip of your finger. Position your right middle or ring finger (whichever is most comfortable) just below your eye and pull down. Position your left index finger on your eyelid just above the lashes and pull up. At this point, you should be able to move your right index finger plus lens directly toward your eye pretty easily until you get the contact into your eye. Just try not to blink as you're moving the contact in.

It might be that you're having trouble getting over the initial flinch reaction of seeing your finger come toward your eye, and catching the contact on your lid/lashes as you blink reflexively? I'm not sure. It's been almost 15 years since I learned to put contacts in, and even after a 3 year break from wearing them I hadn't lost the skill of putting them in.

Also, possibly because opticians are epic sadists or possibly because they do it for lols, often the *first* time you go to the optician to talk about contacts you'll get told a completely impossible way of putting them in. This frequently leads to the mentioned 1.5 hours of frustration, plus some charmingly red and streaming eyes. Go back, explain the problems you're having, be calm, and ask to be told the magical way that actually works ;-)

My pro tips:
1) Do not close the other eye while you're putting a lens in. If you do, the eye you're trying to put the lens into will roll alarmingly and it'll be much harder. Use the waiting eye to help you see what you're doing.

2) Make sure that you're pulling your lids apart dead in the centre, to get the widest aperture you can. Easy to miss.

2a) Also make sure you're pulling the lower lid down far enough. I found it v easy to obsess about how far the top lid goes up and ignore the lower one.

3) There's a ridge at the top of your upper eyelid. Make sure you have that ridge firmly under your finger, as then the lid can't slip away.

4) Don't be afraid (if you have disposables?) of saying 'sod it!' and opening a new pair while you're learning to put them in.

Can you touch the surface of your eye without violent flinching? This may be the easiest way to practice. Use the corner of your eye, while looking away. Generally I try to avoid directly touching the iris or pupil directly. This may or may not be medically sound, but I find it feels weird and leads to freaking out.

Making sure the bowl of the lens has some fluid in it helps, as the lens will float around a bit until it settles in front of your iris, and the extra lubrication makes a difference.

Are your eyes dry as hell? Putting some solution in your eyes can also help.

I have a two-hand, off-hand lead method, which I will describe on the off-chance it will help:

Put the lens on your left index finger, making sure there's solution in it. (I actually bring it toward the pad a bit, so it's sort of in the space on the edge of the tip and the pad.) Pull your eyelid up with the middle two fingers or your right hand. Pull your lower lid down with the middle two fingers of your left hand. I find that my eyes defocus during this phase, which seems to help me concentrate better. Position your left index finger above the center of your eye. Look at your left index finger long enough to make sure it's lined up properly. Look away, up and to the center. Set the lens gently on your eye, on the white. It minimizes the odd sensations and the visual stimulus making you freak out. Keep your finger on the lens as you bring your focus back around to your fingertip. This puts the lens on your iris as gently as possible and helps to minimize the floating around.

At this point I blink furiously, press a towel against my eye, and roll my eye around to make sure it doesn't feel weird. Sometimes you will feel the edge of the lens; I don't know why this happens and I usually take it out and make sure it's not inside-out, and put it back in (after adding solution). It's rarely flipped, so I wonder if it's just a matter of it not settling correctly.

Now, an optometrist explained this to me when I was in 8th grade, so let's see if I can avoid mangling it too badly. You want your eye and the lens to have like wetness. If the lens is dry, it won't stick to you eye, will try to roll or fold, or even pop out of your eye when the lid comes down. Even if you get the lens in while it's too dry, it feels wretched, so you'll probably end up taking it out and trying again. If your eyes are dry, well, mostly it just feels super weird when the solution hits the surface of your eye, and the lens ends up not wet enough, I guess as your eye drinks up the moisture. Best to make sure both are sufficiently moistened.

I imagine that I do most of this by touch because once you get the one lens in, you're fucked for visual stimuli anyway.

I also would be happy to demonstrate if there's a chance before you figure it out.

Putting things in your eye is just wrong. Wear glasses like all the other nerds.

Looks like the other posters have most things covered well. Just wanted to drop in to add encouragement - it takes a while to get the hang of it. It's hell at first. Keep at it. Until you're wearing them every day for weeks on end, you won't approach the ease of experience that the rest of us are at.

You have to pin back your eyelid and pull down the bottom while you're putting the lens in--no way can you do it just with your eyes open normally. The other posters pretty much have the method covered.

Additional tips:

1. Having a mirror helps because then you can navigate by looking at something past your hands--try not to focus on the contact lens as it approaches.

2. To help get the contacts properly seated, after putting in the lens, without blinking, look a little bit left, right, up, and down. That helps get it centered and keep you from blinking it out.

3. Contacts can get inside-out. Make sure the contact lens is a bowl shape. If it is more of a ufo-shape, it is inside-out.

If the eye-touching is a problem, try doing it in the shower every day, softly. Worked for me. Otherwise, I tend to have the bottom of the contact be the part most on my finger with the upper part sticking up. Then I get the bottom near/on the eye and flip the rest onto the eye. There's usually a fold, so I close eyelid, push, blink a lot, then move the contact through lids again if still a problem. Usually, just blinking a lot should do the trick.

If this fails, use the "catching a piece of popcorn in your mouth" methodology. Just toss it up in the air and try to get it to land right-side down on your cornea. It takes some practice, but then you never have to actually touch your eye.