You can not catch a faerie, and you can not "take" their powers. They generally avoid people with such thoughts as it is anyways. I'm sure you could attempt to enact something that you believe would catch one, and upon it having no success, you would probably find yourself with a cacophony of bad luck. Simply because the Fae can cause you bad luck, and because you tried to cause them bad luck, they would love to return the favor.
However, you can form a friendly relationship with them if they happen to dwell or pass by your place of abode. Leaving out a dish of milk and some bread is a good way to show your good will, and like Neko said, you could plant a garden to attract them. But they are beings of vibrational energy to us, and they would sense your ill will in a heart beat. Small gifts are good invitations as well. If you've ever been walking in the woods, and found something like a rock, or piece of bark, or flower that caught your eye for some reason, you could always offer it as a gift to them. Some of them delight in the beauty of what we call simplicity, they see it in a different way.
I've read about people saying they have seen the Fae, however it was unclear if that was in their minds eye or if they actually saw them. On this subject, I always play it safe and assume they meant within the minds eye.
You cannot change your DNA to permit you to grow wings, change your eye color, grow taller or shorter or any other physical change through the use of magic.
I love the discussions on these "nature spirits", now to answer your questions, it depends on if you are talking about little people with wings or the spiritual belief of the fae, none of them exist on this plain, so no you can not physically see them.
Fairies can be seen, as they can manifest themselves the same way ghosts or similar spirits do. In my home, I will encounter many beings, but there is always a small flash of light I can barely see. What makes these lights different from the other spirits is that my youngest brother can see them too, and i'm the only one who has seen anything supernatural in the house. I am certain they are fairies as when I tried to make contact them, Calling them as fairies, I saw a small shadow out of the corner of my eye dart behind one of the couches. I took it as a sign from them.
I have had quiet a bit of contact with Fae,they were the ones to initiate all of it. I have only seen them in my minds eye, to start with they projected themselves as pretty little winged creatures, mainly to let me know who they were. Later they told me they do not look like this, but can appear in any way they wish, by projecting as nursery rhyme fairies people feel more comfortable & less frightened of them. My little boy was rushed into hospital with his appendicitis, due to the ambulance being late, they dosed him up & hoped he could go until morning before having them removed. I have never seen him so ill & was worried about leaving him overnight. I asked the Fae for help & to cut a long story short, by morning after sleeping soundly all night he was 90% better. The dr's were amazed & could not understand how he had been so ill & made a miraculous recovery. when my mum came up to the hospital she immediately commented on Oliver & myself being covered in a very fine glitter. Everytime we removed the glitter, it reappeared. The following day, during meditation the Fae spoke with me & told me they had healed my son & the glitter was just a sign to say it was them.
Then I suggest the book "The Fairy Faith" by W.Y. Evans Wentz. You can find the entire book for free online because it was written in 1911. Just google it. Happy researching.
In my op. Faeries could be entities (spiritual, from the collective counsiousness, ... Not with a fisical body) or could be animal species that primitive people thought have magical powers.
