Hello and welcome! A new house with a pond.....both exciting and daunting! You've come to the right place for help!
Believe it or not, he was right about not having to feed the fish. Goldfish can and do survive perfectly well by just eating the algae that grows on the side of the pond.....as well as catching insects from the surface, etc. Algae isn't a bad thing, but too much of it means that there are more nutrients in the water than your biological system can handle. It bothers us more than it does the fish. You can remove the stringy algae manually, if you choose.
How large is your pond? What are the dimensions and how many gallons? What kind of pump does it have? Is there a filter [it could be inside the pond or outside]? Is there any provision for water movement, such as a waterfall? Is your "source" water [the water you put in the pond] well water or city water?
I would stop feeding, or feed very sparingly. The cause of excess algae is excess nutrients in the water. If you can, add plants. Underwater [submergent] plants will help with the nutrient problem and [during the day time] will add oxygen to the water. Plants where the roots make direct contact with the water [some marginals, parrots feather....] will help. If there isn't any shade covering the pond, water lily pads will cover the surface for shade -- also helping to eliminate algae by blocking the sun [but they don't have an effect on nutrient levels]. So, providing any kind of shade is helpful. Remove any uneaten food.
And the fish might not be eating right now because they're either not hungry or they might see you as a predator [dark shape looming over them....]. If the previous owner never fed them or messed with the pond very much, they don't know that you are a good guy. Give them time. Patience!
You could do some partial water changes, but be sure to add a dechlorinator/dechloramine to the new water. "Topping off" isn't a good idea for routine maintenance, so it's always best to remove old water before you add fresh. I know there will be some who say they never remove old water, and always "top off," but as water evaporates, any minerals or chemicals that are naturally in the water are left behind during evaporation, and the only way to keep these from reaching high [and potentially lethal] concentrations is to physically remove them by removing the water.
Get a pond water test kit and start monitoring your water quality. We recommend a liquid, or "drop" test rather than test strips, and most use API brand. You'll want to test for ammonia, nitrites, nitrates, pH, KH, and GH. At first, just keep a record of the results, but don't panic [freak out/over-react] if your results are "off." Mainly, for now, just get a baseline. Then report those back to us. But always give us the NUMBERS for each test result -- don't say "normal," "fine," or "OK." Oh, and do the same tests on your SOURCE water initially.
As a general rule, we don't advocate the use of CHEMICALS of any kind except for de-chlorinator. Let Mother Nature do her job -- it's just up to you to provide the attention to maintenance [filter cleanings, etc. -- more on that once we know what kind of filtration set-up you have] and the hardest part, which is PATIENCE!