Start from the passenger rear as you did then go to driver rear, passenger front then driver front (basically from furthest from the master cylinder to the closest).
If only air comes out while you are bleeding then just keep pumping. Contrary to the above a simple hose is no good, buy a one man bleeder hose from repco or supercheap (cost maybe 5-10 bucks). Unless skylines have a check valve built into the caliper (unlikely) you can draw air back in through the hose when you release the pedal if you don't use a bleeder hose. You need to close off the nipple before you lift the pedal, the one way valve does the same thing. Thread tape isn't a bad idea though, you shouldn't get air in through the threads but it's better to be safe than sorry I guess.
Ideally when bleeding brakes you should use a different coloured fluid so you know when you've flushed them completely but if your fluid is old it will probably be darker than the new stuff so you should still be able to tell.
Take the top off the reservoir, hook the hose up with the other end in a bottle and undo the bleeder nipple. Pump the brakes until the reservoir is NEARLY empty (not fully, never let it empty below the fluid pickup) then fill about 1/4 with the new fluid. Pump the brakes another few times until the reservoir is nearly empty again then fill it about 3/4.
Now get another bottle and swap them over on the hose (still on the same caliper). Give the brakes a couple more pumps and check the colour of the fluid to be sure the new fluid is coming out. If it's not just keep pumping until it does. If new fluid is coming out, switch to the next caliper and top the reservoir up if needed. Hook the hose up, open the nipple, pump until new fluid comes out then close it up and repeat for the other two.
Hope that helps.