With the Slime-branded kit, you get a bottle of (replaceable) Slime and a compressor. You squeeze the Slime into the tire after removing the valve stem with a supplied tool, then, after replacing the valve stem, you fill it up with the compressor and run for a mile or so to spread the goop around. After that, you may have to top up with the compressor again.
Are you sure? I didn't see a valve stem removal tool nor the can of slime. It's built into the compressor. There's a red cap which gets removed and the tube screws onto the valve stem and the slime is released. Actually the instructions are very minimal.