Question: In the fourth Harry Potter movie, when they went to the Portkey, how did someone put it there without touching it?  

I mean also the triwizard cup, how did the guy put it there without teleporting to the graveyard?

Answer: 
Book Answer
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Portkeys can be set to go at a specific time.

> 
> Almost any inanimate object can be turned into a Portkey. Once bewitched, the object will transport anyone who grasps it to a pre-arranged destination. **A Portkey may also be enchanted to transport the grasper (or graspers) only at a given time.** In this way, the arrivals and departures of great numbers of witches and wizards can be staggered, enabling such events such as the Quidditch World Cup to take place with few security breaches  
> 
> (*[Pottermore - Portkeys](https://www.pottermore.com/writing-by-jk-rowling/portkeys)*)
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> 

We can see this several times in the books.

> 
> “There aren’t any more of us in this area, are there?”  
> 
> “Not that I know of,” said Mr. Weasley. **“Yes, it’s a minute off. . . . We’d better get ready. . . .”** (...)  
> 
> They all stood there, in a tight circle, as a chill breeze swept over the hilltop. Nobody spoke. It suddenly occurred to Harry how odd this would look if a Muggle were to walk up here now . . . nine people, two of them grown men, clutching this manky old boot in the semidarkness, **waiting. . . .  
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> “Three . . .” muttered Mr. Weasley, one eye still on his watch, “two . . . one . . .”**  
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> It happened immediately: Harry felt as though a hook just behind his navel had been suddenly jerked irresistibly forward. (...)  
> 
> Harry looked up. Mr. Weasley, Mr. Diggory, and Cedric were still standing, though looking very windswept; everybody else was on the ground. **“Seven past five** from Stoatshead Hill,” said a voice.  
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> (*Harry Potter and the Goblet of Fire - Chapter 6* - [text available on Pottermore](https://www.pottermore.com/book-extract-long/stoatshead-hill))
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As for the Triwizard Cup, Crouch made it into a portkey *after* he put it down.

> 
> “**I offered to carry the Triwizard Cup into the maze before dinner,” whispered Barty Crouch. “Turned it into a Portkey**. My master’s plan worked. He is returned to power and I will be honored by him beyond the dreams of wizards.”  
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> (*Harry Potter and the Goblet of Fire - Chapter 35* - [text available on Pottermore](https://www.pottermore.com/book-extract-long/i-was-ready))
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The portkey on the hill could easily have been maneuvered to where it was using Wingardium Leviosa or a number of other charms, or placed it there before making into a port key. Similarly, Moody/Crouch made the Triwizard Cup a portkey after placing it in the center of the maze, which he did himself. (On a side note, I'm sure Bart Crouch Jr. wouldn't have a problem if he port keyed to the graveyard, being insane and all.)