or do you just put the next beer right on top of the last beer old hop debris and all.
Sometimes, yes. You can do this and the typical approach is to go from lighter/weaker to darker/stronger beers (e.g. brew a light lager, use the yeast cake for a dopplebock).
Or, you can pour the yeast cake into a sanitized container and wash the yeast as mentioned above.
Or, you can pour it out and use only a portion of the total cake for your next batch which minimizes concerns about over-pitching.
There are several ways to go about it. Find out which works best for you and go with that.