The plan is to use the atmosphere as propellant and beamed power to heat it. This is much a much more effective way to get from the Earth's surface to low Earth orbit than building a huge propellant tank and using enormous amounts of propellant to lift the propellant.
1MW of beamed power puts 1kg of spacecraft into low Earth orbit. Here are some spaceship masses:
4547kg: Apollo Lunar ascent stage. (Takes you from the surface to the moon to lunar orbit).
14696kg: Apollo Lunar descent + ascent stages. (Take you from lunar orbit to the lunar surface and back again).
5560kg: Apollo command module. Holds three astronauts during their trip to lunar orbit and back. Has a heat shield and parachutes for re-entry into Earth atmosphere and a splash landing (Do not try this at home unless you have a large navy to rescue you afterwards).
44776kg: Apollo service module + command module + descent stage + ascent stage. Takes you from Earth orbit to the moon and back to the Earth (well, the sea anyway).
10809kg: Altair ascent module.
45864kg: Altair descent + ascent modules.
8500kg: Orion crew module (Holds 7 astronauts).
66864kg: Orion service module + crew module + Altair
Going to Earth orbit and back would require a 5 to 10 GW laser depending on whether you choose Apollo or Orion kit (Dragon is about 10000kg, Soyuz is about 7250kg). Going to the Moon in a single launch would require a 50 to 70 GW laser. If you can bolt the modules together in orbit, you could cut that back to 10 to 20 GW depending on how good you are at construction in orbit.
A Falcon 9 lifts 10450 to 26610 kg into low Earth orbit, so a 10 to 25 GW laser could do the same sort of things ie resupply the ISS or launch a commercial satelite with a rocket big enough to put it in geostationary orbit.
If you combine beamed power with VASIMR, you can substantially reduce the mass of the service module (20000 to 25000 kg) or low earth orbit to geostationary orbit transfer rocket.