The fridge at 1999 will most likely be an Electrolux model.
They are fixed either by 4 screws, 2 each side, just inside the main fridge compartment and covered with quite large round screw covers, and they go into the surrounding furniture.
OR, by 4 screws through a lip at each side of the fridge at the front, into the surrounding housing.
If the internal fixing, check that there are actually screws in behind the covers !, they are removable with a magnetised screwdriver (Phillips type), they may have just worked loose and need retightening, or replacing if they have pulled loose and enlarged the hole in the furniture, use a larger diameter screw of the same length.(Ensure the screw head will fit inside the recess and the screw cover will go back on..
If the external fixing, use the same idea if the screws have pulled out and damaged the fixing holes in the woodwork.
Other than that, use suitable length screws (about 1/2 inch to 3/4 inch depending on thickness of surrounding woodwork and fix from the outside through the wood into the fridge carcass. Use 2 each side.
Don't use screws which are too long and would pierce the inside of the fridge.