Ammonia can be extremely toxic to fish and cause disease and even death. Regular tank maintenance such as tank cleaning and water changes as well as creating the nitrogen cycle are designed to maintain safe levels, but when ammonia levels spike it must be addressed quickly in order to mitigate its harmful effects and stop further outbreaks of illness or mortality.
Change the Water
To start off, it is advisable to swap out about 50% of the water with fresh dechlorinated tap water, using a siphon tube to drain out and collect old water in a bucket, while slowly replacing it with new dechlorinated water via gradual pour-through of dechlorinator bottles or tap. While this won't directly remove ammonia, it will give you time while you consider how best to proceed.
Check for sources of ammonia build-up such as uneaten food or dead plant matter that might be contributing, and remove it promptly. Altering pH can also make water less ammonia-friendly - though this won't eliminate ammonia completely, it should make it less hazardous and more soluble over time.
Add Dry Rock
Consider adding dry lava rock or another substrate material such as gravel to your fish tank in order to reduce ammonia levels by increasing surface area and encouraging bacteria that already live in your gravel to colonize it further. While this won't provide as effective filtration on a budget, adding extra biological filtering could provide benefits of its own.
Ammonia-removal products, commonly available at pet stores or online, may also help. While they won't actually get rid of all ammonia from your fish's environment, these temporary solutions should help make life safer for your fish. When used alongside other measures to address the cause, such as changing feeding practices.