NASA has chosen Falcon Heavy to launch the first 2 gateway modules
NASA has selected the private company SpaceX to launch the first 2 Gateway Modules. They have selected SpaceX's Falcon Heavy Rocket, their most powerful and capable rocket at the moment, also currently the most powerful operational rocket. The current plan is to launch these two modules NET (no earlier than) the year 2024.
How it will work:
A spacecraft, like NASA's Orion capsule (which is made for the moon), SpaceX's Lunar Starship HLS, Blue Origins HLS (human landing system), or Dynetics' HLS. The astronauts will dock to the lunar gateway and get necessary resources from the space station or temporarily stay and/or sleep there, and then get into NASA's HLS, or a private company's HLS like Dynetics' or SpaceX's, undock, descend to the moon, land, perform the EVA mission, get back in the lander, ascend back to lunar orbit, dock back to the lunar gateway, and get back in the gateway.
After getting back into the lunar gateway, the astronauts will get back into the Orion Capsule (or dragon capsule, starship, or more), and go back to Earth. All of this will be done instead of carrying a lunar lander with you during launch, and docking to it while on the way to the moon, apollo-style.
The Lunar gateway will benefit everyone in several ways, also getting us one step closer to a space fairing civilization, and where millions/billions of people live and work in space.