Bleed the brakes in the normal way and when clean fluid comes out of the line you're doing, move on to the next bleeder till you're done. Since you've replaced the master, you'll be starting out with fresh (clean) fluid. When I bleed the brakes to put fresh fluid in osomething that is best done annually or no later that every 2 yrs IMO), I'll take the old fluid almost completly out of the master and put the fresh fluid in. Saves a bit of time and no sense running the old **** thru.
I flush the brake (and clutch) systems the way lowmileage describes. If there is a lot of cruddy brake fluid in the reservoir, use a syringe to suck out most of the old stuff first. Add fresh and start bleeding it out. DO NOT let the reservoir run dry - that'd introduce air into the system and make bleeding it out again a lot harder.
Use a large enough quantity of new brake fluid to ensure that it iis well flushed. You'll not get 100% new fluid in but it'll be 99% or higher.
Don't try to save a few cents by saving an opened container of brake fluid. Use new. Maybe keep a small (unopened) container for emergency 'topping up'. A properly filled system should have all the fluid it needs for brakes that are new until the pads are worn. If one is needing to add fluid frequently - there is a leak somewhere.
I'm about to do this myself, and what I have read is to start with the wheel furthest away from the master cylinder first (so passenger side rear for a LHD car), than driver side rear, then passenger front and then driver front
If you've got a newer-style fluid reservoir, use the Motive Products pressure bleeder. This is one of those tools I bought a few years ago, and I felt like kicking myself for not buying one sooner. Only downside is that you really do need to have that sealed reservoir, though. While not original, I've got one on my '74 Spider, just so I can use the pressure bleeder.