My answer refers to Tibetan Buddhism, I am not sure whether the same applies to other traditions.
Eye opening ritual is the final stage of a statue filling ritual. A newly bought statue is hollow inside and its base can be opened with a tool. If one sells an already filled statue, it is a good practice to ask in what circumstances it has been filled.
During the statue filling ritual the face of the Buddha is covered. Traditionally, the face wasn't even painted before the statue has been filled. In this case the eye-opening ceremony involved adding the actual eyes to complete the statue. Nowadays it is difficult since many statues are acquired in Asian countries to be sold in the West.
To fill the statue one needs a special transmission to do so. In the West various local Buddhist centres organize statue filling events so that people can bring their own statues and have them traditionally filled. You can see a photo relation from one of such events. I have never heard of anyone filling the statue without receiving special instructions.
Personally I own a two statues. One has been bought and filled in Germany and the second one was bought in Kathmandu and filled in a local monastery. I uncovered the eyes only when it safely arrived to my home and I placed it on my altar. I've been told it is a good practice to cover the eyes of the Buddha during the travel and open it only when you can place the statue at it's final destination.