They sink for 10 feet on the first round
The Aquatic Adventures campaign setting clarifies how this works (page 43):
Buoyancy Speed: A creature begins to sink or rise at the end of its turn the first time it badly fails (or does not attempt) a Swim check, moving up or down as appropriate at a speed of 10 feet; this speed increases by 10 feet each subsequent round unless the creature is stopped, to a maximum speed of 30 feet after 3 rounds. This movement provokes attacks of opportunity as normal. While sinking or rising because of its buoyancy, creatures are considered off-balance (see Off-Balance and Prone Underwater on page 45). Once per round, a creature sinking or rising because of its buoyancy can stop its momentum by succeeding at a Swim check as a move action.
A creature that chooses to continue moving in the direction of its buoyancy under its own power, rather than through uncontrolled rising or sinking, can do so with a successful Swim check without needing to stop first. If a creature’s buoyancy changes instantly while sinking or rising from buoyancy (such as via jettisoning something it’s holding or using magic), its buoyancy speed adjusts by 10 feet in the new direction each round. A creature that fails the DC 20 Swim check to move against its buoyancy while swiftly sinking or swiftly rising moves 30 feet in the appropriate direction immediately.
So, at the moment you fail your Swim skill check, you go underwater and begin sinking. Initially, you sink only 10 feet, but each consecutive round that you do not stop this movement (using a move action and a Swim check), you will move an additional 10 feet, for another of 20 feet on the second round (total 30 feet) and 30 feet on the third round (total 60 feet).
This answer explains exactly how Buyoancy works:
Basically buyoancy makes a creature go up or down when swimming. Whenever they fail a DC check by 5 or more, or when they do not spend any actions to swim, the creature either rises or sinks due to buoyancy. It has three normal states: sinking, rising and neutral.
Land creatures usually have a sinking buoyancy, unless they are carrying a substantial amount of low-density gear (like many wooden items) and little or no high-density gear (items made of metal or stone). The book presents air tanks and gear that can change your buoyancy on demand.
Buoyancy also has two extreme states: swiftly sinking and swiftly raising. If they are swiftly sinking, their carried gear is so dense that they can walk at the bottom of the body of water, and must make a DC 20 check to stay off the bottom. If they are swiftly raising, they must make a DC 20 Swim check to stay submerged, or they will move to the surface of the body of water.
The speed of this buoyancy-based movement depends on your Swim checks. Whenever you fail (or do not make) a Swim check, you move up or down 10 feet, and every turn after the first that you do not attempt to fix that, the speed increases by another 10 feet to a maximum of 30 feet per round after 3 rounds. When swiftly sinking or swiftly rising, a failure means you immediately move 30 feet in that direction. Also, while moving like this, the creature is considered off-balance.
When moving against your buoyancy, your movement is hindered, much like a flying creature flying upwards. As such, each 5 feet of movement in the opposite direction of your buoyancy costs you 10 feet of your movement.