Disclaimer: I disclaim any and all responsibility for anything and everything in this post.
It’s been a while since I started wearing lenses, and I’ll assume you’re referring to soft contacts, as opposed to Rigid/Gas-Permeable lenses, which are different.
Basically, wash your hands with soap and then rinse your hands, carefully, with a special emphasis on the fingertips. Then, put plenty of saline solution on your fingers. Take the lens and rinse it with a little saline. Then, put a drop or three of saline into the lens, if you can swing it (this will lubricate it as it goes on to your eyes, rather than the lens immediately sucking moisture from your eyes, though it depends how dry or moist your eyes usually are).
Now that the lens is ready (the edges should NOT flare outward, by the way; if they do, the lens is probably inside out), place it on to your index fingertip and bring it close to the eye it will be applied to. When it’s within range but before you’ve batted it away with your eyelashes, look up while lightly pulling your lower eye-lid to expose the lower “white” part of that eye. Place the lens on that white area, then release your eyelid as you slowly look down. This will move the lens on to the center of your eye, where it belongs.
Once the lens is in place, blinking is essential to keeping your eyes and lenses moist; you may, anyways, need to carry rewetting drops, which are much more expensive than saline solution, though saline works just as well.