What is it?
Forget bending spoons. After enhancing yourself with Telekinesis, the entire world of Rapture is open to your manipulation. Practically any object not nailed down in the surrounding environment can be pulled towards you and then rocketed forward with lethal velocity. Your arsenal is only restricted by the limits of your mind.
When should I use it?
Anytime. Just because you aren't aware of possible ammunition scattered around you doesn't mean it's not there. Pull down the plasmid trigger and watch as strange and unexpectedly dangerous objects float into view: crates, signs, liquor, tennis balls, syringes, teddy bears, dead cats...
If you're truly desperate, you can even steal the hat or mask right off an approaching Splicer and throw it back in his face. Then, use Telekinesis to whip his corpse at everyone else in the vicinity. Have we mentioned this is the most entertaining plasmid? By far.
Some situations are more appropriate than others. The red gas tanks you see lying around will explode and burn an enemy on contact. The ceiling-crawling Splicers first introduced in Neptune's Bounty toss fishing hooks that can be reversed and returned. Same goes for the bomb-hurling doctors featured in Medical Pavilion and beyond.
Finally, Telekinesis is the only way to grab certain valuable and out-of-reach power ups.
Does it work against a Big Daddy?
Throwing random stuff at the Big Daddies certainly works, but it's a slow and risky process. Gas tanks will do the job better, but you can't rely on finding one at the right moment. Don't worry, though, for the Big Daddies will kindly oblige by providing you with their own ammo - the glowing green grenades they lob so often can easily be marked "return to sender."
Telekinesis also enables you to get creative during these encounters. Didn't get the Big Daddy to walk into your proximity mine? Pick it up and chuck it at him. Not satisfied with the trip wire trap you've set? Rearrange the electric lines without having to lay a hand on them.