Reparability all comes down to the location of the leak and the condition of the waterbed mattress.
First, switch off the waterbed heater.
second, put a towel in each of the four corners to soak up the water. Depending on the severity of the leak, you may have to repeat this.
Third, ensure the safety liner is up over either the frame or side foams to prevent water from coming out of the waterbed frame.
Locating the leak.
Whilst drying in the corners of the waterbed frame try to see any water coming from the edges of the corner seams. These are the most vulnerable points of the mattress. Often the leak is very small and is like a tear drop of water that only leaks when pressure is applied. If you have no luck finding the leak widen your search.
Note. To dry the water you may pull the corner of the mattress back to reveal a layer of water. It is extremely unlikely that the waterbed mattress is leaking from underneath. This water is from around the sides, running to the lowest point. If you still have no luck locating the leak. Take a cardboard box and cut it into strips. Pull the waterbed mattress corner away from the frame and place the cardboard strips in between the mattress and the safety liner. Do this in all four corners then leave it whilst drinking coffee and looking for your waterbed repair kit. Upon your return, inspect the cardboard in the four corners. One will show an obvious wet spot. This will narrow your search. If the leak is on the seam around the neck of the filler valve, unfortunately this will not repair successfully due to being two different types of plastic.
Repairing the leak It is not normally necessary to empty the waterbed mattress, although a leak on the side is easier to repair if about one quarter of the waterbed mattress is emptied by simple siphoning. (See draining your waterbed) A waterbed vinyl repair kit is essential. Having found the leak. Pull the effected area back from the waterbed frame. Wedge something down between the waterbed mattress and the waterbed frame, to hold the leak area above the water line. Remove the waterbed mattress cap and plug. Lift the valve up allowing air to be drawn into the waterbed mattress. Replace the cap and plug, work the pocket of air towards the leak area, this will mean the leak is not in contact with the water. Take a hair dryer and gently warm the local area of the leak. This will soften the vinyl and dry any moisture. Assuming the leak is a small split of 3mm or 1/8th inch, smear glue from the waterbed repair kit generously on the mattress only in a circle of approximately 2.5cm or 1 inch. This will begin to dry quickly being warm from the hairdryer. Cut a small circular patch from the waterbed repair kit, approximately 1.5cm or 5/8ths inch diameter. Obviously bigger than the leak and smaller than the glue area. Place the patch over the leak and with your thumb nail squeeze out any air trapped under the patch. This is easy to see because the patch is generally clear. If the patch is textured place the textured side down. Once the glue is dry, smear some more glue around the edge of the patch to seal it down. Allow at least an hour for this to dry, try not to disturb the area whilst it is drying. Once dry, remove all towels, objects and cardboard from the safety liner. Spend time to pull back the mattress and dry as far underneath as you can reach in all four corners and around the sides. See (Identify the cause of a leak)