I have a 3 of these Delta ball type faucets in my home. Every couple years, I have to service at least one of them, depending on the usage.
You can find the various parts and kits at your local home supply store. I recommend getting the kit, and replacing all rubber parts.
These faucets have a central ball whose movement partially uncovers the hot & cold supply feeds as you move it. There are rubber gaskets and springs on the supply, and there is a cap gasket on top.
If you buy the kit, it typically comes with a tool that includes an allen wrench to remove the lever. In your case, pop the cap and see what is holding the knob on. Once the knob or lever is off, you need to loosen the crown cap, a special spanner wrench does that. Once the pressure is off, you should be able to loosen the crown ring. After badly scratching one faucet, I always use a fabric strap wrench to do this.
Remove the ball, and inspect it for wear and smoothness. The ball shouldn't need to be replaced very often, but if you have a heavily used faucet, they make metal replacement balls. Look in the bottom at the supply gaskets. Pull them out with a screw driver. Put replacements back in. The cap that holds the ball down has a rubber face and wears out over time. You reassemble everything and then tighten the crown gasket down. As it breaks in, you may want to re-tighten it after a few weeks. It may feel stiff at first, but you need pressure to keep the seal.