I´ll try to create a good telekinesis ability here.
Assumptions: Nen user is Emission type, has a good concentration capability.
Telekinesis
You send aura to an object (living or not), in a way that the aura will involve the entire object.
Condition: You have to stare at the objetct for a while, concentrating on it. The longer the stare, the more aura acumulates in the object, and the easier it gets to manipulate it. If you stop staring, the accumulated aura will stay, so you can choose to keep the concentration (even while levitating) and increase the control, or concentrate on other things, while maintaining control over the inicial object.
So, the heavier and bigger an object is, the harder it will be to levitate it, because you will need a bigger amount of aura to put it out of the ground. Also, direct eye contact must be made, so no moving internal organs and shit.
There, I am levitating stuff. There can also be conditions for living beings, if one feels necessary.
For the Manipulation type is harder, because from what i´ve seen, they need some kind of link to the manipulated (ex: Illumi´s needles). I wanted to make a hatsu that needed no direct contact.