Where should I put the punctuation?

Neither. In this case, we are talking about programming, and "strings". It should be specific. If we aren't putting in a "." then we shouldn't say we are going to see one, even if it's grammatically correct.

When learning how to program, it is incredibly import to convey how sensitive the syntax is. Evey period (.) comma (,) semicolon (;) etc must be used with care. This is one of the common mistakes beginners make when learning how to write code. Forgetting to use a period in the middle of the syntax, or putting one where one doesn't belong can throw off the entire intended operation. So, to aid the experience of someone who is trying to learn such a specific skill, all of the documentation should he as clearly written as possible.

While adding the period to the end is grammatically correct according to the Yahoo Manual of Style as stated in another answer, why take the chance of introducing confusion if we are trying to drive home the point of how important periods are in a programming syntax? The simplest and most straightforward approach should be favored here, after all we are trying to help someone through a difficult and mentally exhaustive process. The easier it goes, the better.

To take that even one step further, you should remove even the quotes around "Hello World" and use italics, bolding, or color to emphasize the output.

I would also restructure the sentence so that the "Hello World" is not at the end. For example:

You should see Hello World on the screen.

This way you avoid the situation entirely.