What are the books usually called for studying the computation of GDP?
It seems that the economics growth by Barro doesn't discuss about that.
The ultimate reference is the UN's SNA 2008 manual. SNA stands for System of National Accounts. The SNA 2008 is the international statistical standard for the national accounts
Blanchard, Macroeconomics 6th, p. 20 is a good and easy start. If you want more, then yes good directly to the office' publications. The BEA has a very complete documentation.