Which one is correct?
This is what I want to put in my application for a Russian visa.
Use the first on your application: 'I want to know how large Russia is.'
The other is also grammatical in contemporary English, but it means something different. 'I want to know how large is Russia' asks the question 'How large is Russia?' and gives the reason for asking it as: 'I want to know'.
Either is fine as a statement. As a question, one would ask, "How large is Russia?" but not "How large Russia is?" I mean, it would be understood, but it would be obviously non-native.
I would agree with the other answerers that the first is a better choice, but I'd also amend the second to read, "I want to know - how large is Russia?" if you want to use it.
This way, you're using the commonly-accepted verb structure for questions, while separating the question from the reason for asking it. It's probably not appropriate to include a question in your application for a visa, though, so the first phrasing is still the better choice.
I want to know how large Russia is.
is the standard way to say it.
If you are a learning English as a foreign language, the second one will sound foreign (and should get a red X if you use it in class).
You may notice I'm not saying 'wrong'. It is normally considered wrong but there is nuance here. The other way, "I want to know how large is Russia", is often said by native speakers anyway but is more of an infelicity or a processing error; the speaker has changed their mind in the middle and is now actually asking the question (as show in writing by inserting a hyphen in the middle and a question mark at the end).