To draw on historical analogy, 19th century frigates and ships of the line were state-of-the-art floating cities carrying huge stocks of spare parts. They had the tools and expertise to make all sorts of repairs, smelt and shape metal, and even fashion new masts if the material is available, and large crews for the labor. Their spares and crew could be supplemented by capturing enemy vessels ("prizes") or sending shore parties to fetch lumber. In extreme cases, naval vessels would make unplanned circumnavigation of the world in pursuit of prizes or to avoid capture.
Moving forward, the Galactica is more like a WWII aircraft carrier or battleship. They are also floating cities with large, skilled crews and well-stocked repair bays. Major damage such as knocked out boilers and holed decks could be repaired at sea. Their aircraft could be serviced, repaired and stripped of spare parts. They also had a fleet of attendant supply and repair ships, much like the Colonial Fleet. Even the idea of building a new aircraft is not entirely far-fetched.
As an example of the sort of pounding a WWII aircraft carrier could absorb and repair, the USS Yorktown was hit by two torpedoes and four bombs at Coral Sea causing fires and flooding with an estimated weeks of repair. After just two days repair she put out to sea to fight the Battle Of Midway. Hit by three more bombs, she was dead in the water. An hour later, she could make 20 knots and was ready for flight operations. She took two more torpedoes in another attack and lost power but still didn't sink. While repairs were underway, two more torpedoes from a submarine finally broke her back. It still took her until the next morning to sink.
About the only thing which cannot be repaired is damage to the keel and other major structural damage. Once a ship's back was broke, only dry-dock could allow weight to be taken off the keel for repair. Galactica, being a space ship, does not have this problem.