Placing Tree..!

Put a peg in the ground.
Tie a string to the peg.
Tie a screwdriver to the free end of the the string.
Pull the string tight and scratch a perfect circle on the ground using the screwdriver.
Draw an 'X' through the circle and make sure that the centre of the 'X' is where the peg is. The 'X' must also be made of lines that cross at right angles.
Put your trees in the four spots where the 'X' crosses the arc of the circle that you have drawn.

Arawn,

Wouldn't that place the four trees at the corners of a square?
The distance between the diagonals wouldn't be the same as the distance between two adjacent corners.

I was trying to describe the points of a tetrahedron.
I think that the mention of trees is to coerce you into thinking of a two dimensional answer and there isn't one. >'equidistance from each other'

I wasn't sure if the guy was giving an actual puzzle or he was giving us a landscaping question.  I thought it was a landscaping question which is why I answered with details about how to actually scratch a circle into the ground with a string and a screwdriver. I think you might be right though that this is an actual riddle, in which case your method would work, providing there is a hill or a pit nearby.

You could have the trees indoors in tubs, then you wouldn't need a pit or hill, just put one on a different floor.

But then you would have to get a Feng Shui master to help you align them and that might bugger up the distances. ;-)

2 separate solutions'

The complex one---------
One Tree at a Pole...
Lets say North Pole...

Now the other 3 trees should be equidistant from the tree at the north pole and each other...

SO we place them on a circular crossection of the earth which is parallel to the circular cross section containing the equator such that the distance between them is 2*pi*d / 3 where d is the radius of the  circle. and the distance between the pole and each of them is the same...

The distance between the Pole and any tree would be the same and this would be

(( pi /2 ) - arctan(d/r) )r

solving we would get the exact value...
 
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A MUCH simpler technique would be to consider a pyramid with the traingle as the base...of course that doest represent the earth due to its sharper edges...but use a pyramid each face as an equlateral traiangle...

now take the 4 vertices and plant a tree there...

chop them down and build a bridge out of them.

oh sorry, this isn't the lounge.  ;D

The accepeted answer is wrong. You can not place 4 points equidistant from each other on a flat plane. You can however if you have a hill in the yard and use the concept presented by nrip.

...sorry I misread the post, it is correct.