Create item from Item Template programmatically in Visual Studio

Question

I am developing a VS extension called WebLink, that replaces integrated VS browser.

I'd like to create a command, which would do the following, if a solution is loaded:

1. If current solution does not have a folder named "Links" at the top level, create it.
2. Create a new file in that folder, using an Item Template I ship with my extension, named new tab XX.website (the file should be placed in SolutionDir\Links\ )
3. Open that file in the document well

My problem is with 2: how do I get VS to create a new file, and use the specified item template for it?