Every empty house on the map in Valdera, Orvana and Nyxera is already open for bidding right now -- there is no "release date" to wait for, and no need for a current tenant to move out first.
Finding a house: the Houses page lets you search by city and filter by status (up for auction / already rented / all), by type (regular house or guildhall), and sort by name, size, rent, current bid or time left on the auction.
Placing a bid: go to your Account page, pick a character that is in the same world as the house, and enter an amount higher than the current bid. The first bid ever placed on a house is what starts the clock: the auction closes exactly 7 days after that first bid, not from whenever the house became empty. Every bid after that must beat the current one.
Winning it: whoever holds the highest bid when the auction closes wins -- but ownership is only actually granted at the next server save (daily, 05:00 CET) after closing, not the instant the clock runs out.
The part that catches people out: at that server save, the game checks your character's depot (not your backpack, not your inventory -- specifically the depot) for your winning bid amount plus the first month's rent, added together. If that money isn't sitting in the depot at that exact moment, you are handed the house and then immediately lose it again in the very same process -- and you get temporarily blocked from bidding on any house for a while. Have the full amount (bid + rent) in your depot before the auction closes, not just before you plan to log in next.
If you do have enough, it is debited automatically, a welcome letter appears in your depot confirming it, and your first 30-day rent period starts counting from that server save.
Rent, after that: due again every 30 days, also debited automatically from the depot at server save. If the depot does not have enough when rent is due, you do not lose the house on the spot -- you get a warning letter with a one-week deadline instead. Only if the rent is still unpaid by that deadline does the eviction actually happen, your belongings get cleared out of the house, and you lose it.
Other ways a house can be lost, even with rent fully paid: the owning account loses Premium status (houses require Premium to hold), the owning character gets deleted, or -- for guildhalls specifically -- the owner stops being the leader of the guild the house belongs to. All of these are checked automatically at every server save.
Giving it up on your own terms: an owner can transfer a house to another character in the same world for an agreed price, from the Account page. The transfer is only carried out at the next server save, and can be cancelled any time before then.