When I bought my new house the owners left a pond with ten goldfish(?)
in it and it has gradually become dirty and full of algae. It never
had an electric filter system and I can't afford one, so is there a
way I can manually clean the water?

I'm thinking perhaps I could scoop out bucketfuls of water and filter
it through something like cotton wool, layers of muslin or sand (or
all three?). Can anyone offer any advice please?