Traditionally, toasting honors in Japan are reserved for the host and visitors are not expected to reciprocate. It’s usually delivered at the beginning or end of the dinner party. The first time you meet for drinks the toasting honors will go to the most senior person in the hosting party and will usually be a standard “kampai,” which means “cheers” in Japanese.
With alcoholic drinks, the Japanese consider it polite to serve each other, and not yourself. Your job as a good guest is to periodically check your neighbor’s cups and keep topping them up (don’t worry, someone will be doing the same for you). And if someone wants to serve you alcohol but your cup is full, the polite thing to do is empty it out quickly and offer your cup for a refill.