There was a discussion on this not long ago. The link is below. One of the things to consider is the source of the oil film. Could it be the pump? What kind do you have? Some don't have oil in them, some do and can possibily leak.
Anne

Here is a link that might be useful: Oil on Pond

I've noticed that my lily leaves when turning brown & going bad (decaying) will have an oily looking residue about it ... could it be decaying stuff, plants?

If it's not alot you could try floating paper towels or maybe newspaper .... don't leave it in there ... put it on there, let it soak it up & remove it.

As mentioned above, float paper towels to soak up the oil, but you need to find the source. The pump is the most likely culprit, and it may have a slight petroleum smell. If it is the pump and it's new, take it back for a replacement or a refund.

A really good way to get the film off the top is to overflow the pond, if the configuration of your pond makes that possible. Like others have said, you do need to find the source. Has anyone been using a chainsaw or lawn mower near the pond lately? Those two machines often discharge an oily exhaust.

If it is your pump, don't panic the oil used in pond pumps is non-toxic mineral oil and will not harm your fish or plants.
There are not many oil filled pond pumps on the market now as there used to be.
Most newer submersible pond pumps are magnetic drive and do not use oil.
The oil you see, could be from decomposed plant material or from some new addition to your pond, rocks or plant pots soil, etc.
Flooding the pond over will float the oil off the surface quickly.
"Horton"

I want to thank everyone for helping me out with this' I was so upset I couldn't think, 3 of the fish' I've had for almost 6 years.But did like you said and let it overflow, found out it was veg.oil, I catch rain water for
my garden and I put veg.oil in it to kill bugs and I use a
pump to pump out the water and I found out that someone was
trying to help me and well' you know. But so far all of my fish are doing great.If any of you would like some seeds or a gourd for bird house or a luffa sponge,just let me know.
Thank you - spider

Glad everything is ok.

I am glad everything turned out OK.

I put some gold fish in my pond and i have two problems one is a turles the other is a oil film thats around the edge of the pond our pond is a good distance from the house.We made trail last year and cleaned around the pond so our grand kids could enjoy it.I don't know a lot about a pond but maybe i can learn. Clara