The San Salvador was built in a parking lot temporarily given to the museum for the purpose by the Port Authority. There were some serious problem with the initial construction methods they wanted to use, and it ended up in a lot of wasted time and money. Initially they'd planned to use laminated frames that they were going to make onsite, I forget the wood they wanted to use, but I want to say it was some type of oak or pine. The bonding material they were going to use simply didn't work. Most of it didn't bond properly to the wood, and even when it did it had trouble handling the stresses. The manufacturer sent someone out to make sure it was being mixed and applied properly, which it was; but it still wasn't working as advertised. Last I heard there was the possibility of a lawsuit if the manufacturer didn't refund the museum, not sure what happened with that though. In the end they used live oak frames, and some (very expensive) purple heart for other components of the structure. Now for the pictures, I put them in links because some are quite large.
Once they got all that sorted out, they could actually get started: http://i.imgur.com/kKIk7Gh.jpg
After they got started things moved along fairly quickly. There was a core paid shipwright staff supported by many of the museum's volunteers: http://i.imgur.com/XBL07jm.jpg
Started planking: http://i.imgur.com/tp8uG3s.jpg
And a recent shot with everyone who worked on her: http://i.imgur.com/0uWwBvU.jpg
Close up: http://i.imgur.com/6InPotp.jpg
Once she was completed, they had to figure out what to do with her. This has been another fiasco, they finally settled on something like Plan G to get her into the water. Originally she was going to be put on a trailer, towed down Harbor Drive, and craned into the water; this is the exact same route and method as they used to launch Californian in 1984. That didn't work out for various reasons, and lots of other plans were created and scrapped. Some involved the Navy, some involved an enormous floating crane from LA. Finally they settled on a plan to get San Salvador onto a barge and launch her with the TraveLift at Marine Group. So first, a company that moves houses and other buildings was brought in to lift the ship and rotate her 90 degrees so she was inline with the barge. Here's a picture of them preparing for that: http://i.imgur.com/ZjQZoi4.jpg
Then they had to get her onto the barge: http://i.imgur.com/t2Ucf03.jpg
Which they did: http://i.imgur.com/UycudGf.jpg
Then she went on her first short trip past Naval Base Coronado: http://i.imgur.com/kab7AQb.jpg
Into the TraveLift at Marine Group: http://i.imgur.com/T7QyDxE.jpg
Then to the first picture I posted earlier. Hopefully we'll have more news about an actual launch. Let me know if you have any questions.
She's a modern ketch by the look of it, I don't know anything about her.