They lose the Humanoid traits, which aren’t much
Literally the only thing that they lose, since they presumably have class levels, is the need to eat, breathe, and sleep. Which they will probably get back by whatever type they gain.
They gain the traits of their new type, whatever they are
For example, if they gain the Elemental type, they get the Elemental traits, to wit:
Immunity to poison, sleep, paralysis, and stunning
Not subject to critical hits or flanking
Inability to be raised with the usual magic
Proficiency with simple weapons
No need to eat, sleep, or breathe
- Does the character suffer changes to their stats?
No, their stats do not change. Those are features of their base scores, their race (which they keep), their levels, and their items.
- What about their hit dice, saves, etc.?
If they have Racial HD (which basically no Humanoids do), then yes, but if they only have class levels, then no.
- If the character gains a level do they get hit dice and saves from their class or their type?
Their class, always. Only monsters can advance with Racial HD (i.e. the ones defined by type).
- Are the character's class levels replaced by monster levels?
Not from that card, no. Those are aspects of your race, not type.
With all that said...
The deck of many things is notorious for destroying campaigns. Most games don’t last long after the first card has been drawn. The effects warp things massively, derail whatever was going on, and are often just too absurd to maintain a serious game. For a silly, off-the-wall game, particularly one that’s intended as a one-shot or quick campaign, the deck of many things can be awesome. But if you want to maintain a game for an extended period of time, or want it to be any kind of serious, I advise against it.