(Since so little actually happens in this play, here's the very short list of things James actually does. If you want a timeline of how his character develops through conversation, which is more important to a play like this, head to the "Detailed Plot Summary.")
James comes into the living room after breakfast and hugs Mary. He chats with the family.
He goes out to do some yard-work with Jamie.
James comes back late for lunch, since he was outside chatting it up with Captain Turner.
When he does come back, he grabs a quick drink, and the family sits down to lunch.
After lunch, James goes to the living room again. He answers the phone when Doctor Hardy calls.
James stays in the living room until right before everyone leaves for town at the end of Act II, and then leaves with Edmund and Jamie.
With a few drinks in him, he comes home with Edmund a bit before dinner, and they talk with Mary until James goes to get another bottle of whiskey.
James returns right after Edmund departs, and is left to eat dinner alone, as Mary has gone upstairs.
He spends the time between Acts Three and Four in the living room, drinking and playing solitaire, and only steps out briefly when Jamie gets home so that he can avoid speaking to Jamie.
James comes right back once Jamie falls asleep, and he ends the play at the living room table.