SpaceX is contracted to provide a lander, which they plan to be Starship. The idea is they will land it vertically on the moon, similar to their boosters. No catching it like they do on Earth. Then there will be some kind of lift to get the occupants down to the surface.
They are a long way from making it happen. They need to get Starship reliably to orbit, so that they can launch with a payload of fuel. Then they need to perfect in-orbit refuelling. Then trans-lunar injection, lunar orbit rendezvous, and finally landing. Then get it man rated. The idea is for the astronauts to get to lunar orbit on another ship and then transfer, but that depends on other vehicles being available for that.
Blue Origin are also providing a different lander, but are also quite a long way from having it working. SLS and Artemis are both floundering.
Meanwhile the Chinese are working towards a more conservative system. They will do a lunar orbit rendezvous between the lander and crew craft, each of which will make its way there independently. That allows them to use smaller, existing rockets, and the combined vehicles can be a little larger than Apollo too. They have been showing off the lander prototypes for a while, and testing seems to be going well. They have experience from their space station of longer duration missions and life support systems. Their lunar surface suit is coming along well too. They want to land by 2030, which is believable based on their progress so far, and given that they don't have nearly as much to develop as NASA does.