This is pretty straight forward. You really should pickup the small spiral bound checklist and do this step-by-step, but ignore the bit about setting the flaps in the G450. See Step 9 for the reasoning behind this.
Everything here is from the references shown below, with a few comments in blue.
[G450 Airplane Flight Manual §2-01-10]
All photos from Haskel's cockpit
You had to unlock and move the interior door to get to the LEER and Left PDB, when you move the door back to its stowed position, don't forget to lock it again. (If you don't it will come crashing aft during takeoff.)
Press the Emergency Power ARM switch and verify both of the ON capsules are lit and . . .
. . . the pilot's Audio Control Panel should be powered
. . . the pilot's clocks should be powered
. . . as well as the copilot's clock.
The EBDI and SFD should be powered. MCDU #1 should display fuel quantity (the engine data will be dashed when the engines are not operating)
MCDU #3 will display backup radio information
Unless the main cabin door has been opened more than once since MANUAL mode was selected, this should just require deselecting MANUAL mode, since with WOW the auto mode will drive it open.
You will need to cycle the parking brake a few times to get to the accumulator pressure, which should read 1200 psi at 70°F, varying 25 psi for each 10°F multiple.
Yes, this works just fine in the G-V/G-550, but it doesn't in the G450. The Operating Manual once called for using the EMER STAB and now calls for using ALT FLAP. Both procedures often result in a FLAPS FAIL state. You should leave the flaps where they are until you have AC power on the aircraft.
Gulfstream G450 Airplane Flight Manual, Revision 35, April 18, 2013