How do I repair my kitchen floor?

There is no safe way to do an inexpensive repair on a hole that goes all the way through the floor. You need to replace the subflooring, usually a 4x8' sheet, but could probably get away with just cutting out that area, reinforcing the edges by placing a 2x4 between the floor joists. I'm probalby not explaining that well, but I am sure there are Youtube tutorials. You would want to make sure to get all the bad stuff. The next thing would be to find out why that happened. Is there water pooling? Is there termites? Even with lots of wear, holes usually don't just appear in the floor, there is generally a cause.

You might want to go below and support the weak area with new structure. It's hard to tell how large the hole is or how bad the damage is over the internet but supporting from beneath is the easiest. If you are going to over-lay with plywood before tile then cutting the hole from the top and replacing the broken wood is easier. There should be 2 layers of hardwood under what's there now.

we repaired a floor once by using cement cinderb for support then wood sheeting then tile. That was about 30 years ago. Still holding up