Clamp off the pipes at the reservoir remove the res wash it out with petrol, make sure its dry before you refit it. Fit the feed hose and using a piece of old pipe block off the return spigot at the res else you will have a nasty mess

Refill res with fresh fluid. Using a funnel connected to a drain tray place the end of the return pipe from the rack in the funnel mouth, start the engine and turn the steering from full lock to lock slowly, pause at the end of each turn, make sure to keep the res topped up at all times. Do this until you get clean fluid returning out of the pipe, switch off remove the bung and reconnect the return feed to the res. check levels and everything for security and thats it.
Personally I do this with the wheels turning plates on the ground but I cannot for the life of me think why?

Old habits etc.
If in doubt there are some You tube vids that cover it just dont let the system run dry.
As Mike says you should have the track adjusted too as you have fitted new arms.
P.S. you may have some fine bubbles appearing but these will sort themselves out.