It's been a constant struggle but we've finally figured out something that works for us.
The algae and slime feed on organic material. Keep everything out that you can - leaves in the Fall sink and rot on the bottom becoming a nutrient dense stew for the algae to chow down on next Spring. Ditto grass cutting in the summer - make sure you point the mower AWAY from the pond. Grass cuttings this year become next year's algae food.
We dump our wood ash from the wood stove into the pond all winter - the lye changes acidity ( the pH ) and disrupts the growth cycle of the scum. You have to be careful with this and/or chemicals you purchase as too much change to acidity too quickly can kill off fish/frogs/turtles and other wildlife.
There are 4 large (and large means 20+ year old, 30 pound) "grass carp" scavenging organic matter from the bottom to keep organic material down. These are considered an "invasive species" here in Ohio, and have to be bought from licensed fisheries sterilized, so they don't breed and send little fish downstream to the next pond when it floods.
Even with all that, come late May early June we have a large bloom of nasty stuff. It's from the farmer next door. There's a 90 acre soybean field that drains into the pond via a creek inlet. When Ray (the neighbor) seeds the field and does his fertilizing, the first rain floods Nitrogen into the pond that causes an explosion of growth. For this we use Copper Sulfate - it's a salt ... but heavy metal (copper). Some don't like it but it's considered "organic" because it's a natural salt and not some man-made chemical like Roundup. You have to be careful not to over use it - copper build up will kill worms, snails, slugs, and the like disrupting the food chain ... but it works for us.
There's about a week when we see growth right after Ray fertilizes his field, but before the Copper does its job. Other than that, it stays pretty clean.
If you go with the Copper, look around at farm supply places. The 5 pound is ridiculously priced - we use 10 pounds a season (2 acres of pond, average depth 9 feet). Starts getting reasonable when you purchase a 50 pound bag (or more). 5 pounds at $7 a pound or 50 pounds at $2.50 a pound? Easy Peasy /. no brainer - get the 50 pound bag. Stuff lasts forever and doesn't go bad. A small pond might only use 2 pounds a year.
The real key for us, though, has been the organic matter. We used to just let the yard leaves blow around and settle into the water - there's a couple dozen trees in the yard around the pond. Now, we scoop them out with a pool skimmer every fall/autumn and that has been our biggest bang for the buck.
Easy Peasy