When you damage your vessel, hull integrity will update and be displayed on your HUD in a color coded manner.

• White - Everything is fine
  
• Yellow - The hull has some holes and it is starting to sink slowly
  
• Red - Panic, sinking imminent, the boat will quickly fill with water

Assuming you did not sink to the bottom of the ocean or an otherwise unrecoverable location you can still repair your boat.

Surprisingly all you need to repair your boat is a welder (it even works on wood!). Welders will start in your inventory in sandbox mode and can be purchased from certain buy shacks. You can equip it with right click from your inventory.

Once equipped you can move near the affected area and use the welder to repair over time.
Note: I had to use my nose to get this screenshot

Once repairs are complete your vessel will slowly be drained of water and once again buoyant!

• Repairing the main hull of your vessel can repair everything but at a much slower rate then directly repairing the damaged part such as an engine or wing.
  
• If all or part of your vessel has been destroyed that section cannot be repaired.

When a section of the boat is damaged and on fire, it cannot be repaired until you extinguish the fire.

Fire extinguishers can be found at various buy shacks.