It seems that the information on how to actually structure code when writing Typescript is next to non-existent.
I want to make a server in node. It has external dep
Multi-file external modules are not supported yet in TypeScript.
For module structuring recommendations, this page has a good rundown of the options. In particular, if you have exactly one class per file, you can use export = so that the second line of code in your example would simply be var vec = new vector();, which would be reasonably straightforward.