Hi, I'm trying to build a static grass applicator using this tutorial:

For this purpose I bought this negarive ion generator from ebay :

Spoiler

http://www.ebay.com/itm/201765577659?_trksid=p2057872.m2749.l2649&ssPageName=STRK:MEBIDX:IT

I have almost no knowledge in electronics, so I don't know what to do with the extra wire that my generator has. Could someone please guide me in this matter please?

 

The video shows how to connect the input power and the two high voltage wires.
From your link:
Note: Small red and black line is input, red is 12V power supply positive input, black is negative input, thick red line is high voltage positive output, thick black line is high voltage negative output.

 

Do I see 5 wires on that voltage generator?
If you have a naked wire on the input side, it is a safety ground, which has no purpose for you.