Well, recycling old adaptors is not a bad idea, anything that will enable you to plug small electronic devices to the wall, such as handheld game consoles, walkmans and the like, radios can be a good candidate.
There should be 2 wires, one positive (usually red) and one negative (usually black), if there's another one, it's likely a "ground" or something to evacutate the static energy.
Just remove the plastic coating at the end of both your fan's wires to reveal the metallic wires underneat and twist them together, do the same with the end of your adaptor's wires.
Then twist both positive wires together (the white wire on you converter should be positive) and tape/isolate them well with electrician tape (a smooth black adesive). Do the same with the negative ones. If your fan has more wires (usually yellow I believe), seal it up with electrician tape and leave it alone.
Now plug the adaptor on the wall and see if it works.
...That doesn't sound very clear does it? I'll try and make a diagramm about it.