Appropriate Substitution Addition Question

ASA Rules, Section 4.3 says, "Eligible roster members may be added to the available substitute list any time during the game."

I have a game from last Friday that is suspended due to weather. We are bottom 4th inning, 1 out, runner on 1st. We are the home team, trailing by 1 run. My starting pitcher from that game will NOT be available for the continuation, but another player/pitcher who wasn't on the original lineup card will be.

What is the proper way to address the matter with the umpire if I want the new player to be placed onto the sub list and inserted?

Do I just say, "Blue, before we begin, I would like to add this player #X to my substitution list and insert her as a substitute for player #XX" etc.? Or does she need to wait before she is entered as a substitute?

Just inform the umpire prior to the start of the game you are adding X number of players to your lineup and then you are subbing player X for player Y.