I won the auction for a new Power Plant. I already have 3, so I need to get rid of one of them. Can I put resources from the plant I'm discarding on the plant I just bought? Do I need to store them for the duration of "transfer" on one of the plants I'm not getting rid of? Or do I lose resources when discarding the plant?
You may keep the resources, as long as the new plant can store them. According to the rulebook:
When a player buys a fourth plant, he must discard one of his other power plants. The player may move resources from the discarded power plant to his remaining three power plants, if they match the resources used by one or more of the retained power plants.