It's been a while since I've played it, but I think I remember the key points. Choose your character and mode, and when you're on the course, press 'A' to start the swing. Press 'A' again when the line reaches the end, and one last time when the cursor gets to the starting point again. Before you start the swing, you can press 'B' to switch to Power, for more distance. If you get a perfect swing, the counter for how many times you can use the Power doesn't go down. When you're close to the green, you can press 'B' for Approach, which makes you hit under the ball to reduce the roll of the ball. When putting, you can choose either a light, medium, or heavy hit, depending on the distance from the hole. One of the displays on the side will say either Up or Down, and how much higher or lower the hole is from you. I don't remember too many other things. If you need something else, I'm sure there is someone else who can be more specific.
Oh, and those other people are just random characters made for the game.