Vaxholm is not far from Stockholm...
When it comes to Stockholm, the easy way from St. Petersburg is through the Finland by two ways: by ferry from Turku or Helsinki (1 day), or by plane from Vantaa Airport (1 hour). If we talk about the cost, oddly enough, they are about the same, especially if you buy low fare ticket prior a couple of months before the planned venture.
After that you'll need to get to Vaxholm. There are two ways too: bay Cinderella steamship from Strandvägen (~ 1 hour) or by bus #670 from Tekniska Högskolan (40 min.) The bus will be cheaper and faster, but the boat will be a little longer and cool...
No relax in Vaxholm! The fortress is situated on the island. There is something like "vaparetto" (water bus in Venice) in summer, and also you can call for a little more expensive water taxi. If you have no money, you can swim about 200 meters by the sea...
About fortress's open hours and entrance fee you can see at museum website.