I don't wear contact lenses anymore, but I used to when I was very shortsighted, prior to getting Lasik. I now have better than 20/20 vision and honestly I could not recommend Lasik enough - I don't believe I had significant astigmatism, but really it's irrelevant if you have astigmatism or not, the laser clinic will do a whole battery of their own scans on your eyeballs first and correct whatever needs correcting.
You do hear the odd scare stories and definitely it has been more of a risk in the past, but objectively today the technology really has an extremely high success rate and is improving all the time. I really think the time will come when Lasik or some future iteration of this technique is such a bog standard and quick procedure that it will be performed in minutes in high street opticians rather than prescribing glasses, probably even to children.
One note of caution however - in my experience the clinic can make a difference, there are a couple of big chains that are offering constant promotions and low prices, but if you can afford it, it is 100% worth paying a little more, there are some specialist clinics which don't really advertise and charge higher prices but (in my experience) have higher success rates and just a better outcome overall. I actually was only able to get it done at one of these places in the end because I have another complicating eye condition which meant the big chains didn't want to touch me, but my friend had it done at one of the cheaper places. Fortunately it went well for him also but it sounds like he had quite a different experience in both the procedure and recovery, myself there was basically no pain, hardly even any irritation except in the few hours immediately following the surgery - however my friend had several days of bloodshot inflamed eyes and the procedure itself sounded a lot more uncomfortable. Of course realistically the difference in risk is going to be a few fractions of a percentage point, but you don't want to take a chance with your eyes, IMO.
Anyway, regarding contact lenses
- what I used to do was take the lense out and balance it on the end of my index finger like a little bowl, then, standing in front of a mirror, I'd use the middle finger of the same hand to pull down my lower eyelid, and use my index finger to place the lense just slightly underneath my cornea. Because the lense will be wet it should adhere to your finger while you're moving it towards your eye, and when you get enough of it onto the surface of your eyeball, you should just be able to take your finger away and it will stick. Once you've done this you can let go of your lower eyelid and look down (so that your cornea goes towards the lense). Contact lenses are designed to sit on the cornea and not move around too much for obvious reasons, so you don't need to place them directly ON to the cornea when you're putting them in - once you've got them onto the surface of your eyeball you can usually get them in the right place just by moving your eye around, and the cornea is the most sensitive part of the eye so if you're not used to putting them in this will be a lot harder.
Of course, there's no getting away from the fact that if you've never worn them before you'll have a blink reflex when putting anything in your eye that is hard to suppress, but keeping your eye open long enough to place the lense in it is just something that will become easier with practice.
Hope this helps!