Aluminum recycling is the big win. That sometimes pays for the rest of the operation.
You have to separate the aluminum from the ferrous metals, so pulling out the ferrous stuff with magnets doesn't add cost. Scrap steel isn't that valuable, but there's no problem selling it. Steel mills will take it all.
Pulling out glass and making it into cullet is common, but there's more glass cullet than glassmakers need. Sorting by color is possible, but adds cost. Works fine, though. There are uses for low-value mixed cullet, mostly as fill in construction, so it usually doesn't go to the landfill.
There are advanced sorters that can separate the major categories of plastics, but they're still rare. Plastic bottles can be recycled all the way back to plastic pellets for new bottles, and a huge plant near Los Angeles does this for most of Southern California. Not clear that this pays without subsidies.
Paper recycling from post-consumer waste is tough. It's mostly low quality packaging material, which can at best be recycled into lower-quality packaging material. The fibers get shorter each time around. Recycling paper from offices, and recycling newspapers, used to be a thing, but those sources are in decline.
The US recycling industry is currently struggling because China will no longer take the unsorted paper/plastic mess that used to be sent there in empty shipping containers going back. That will probably get worked out.