While this SE site is a good source for getting specific questions answered, where can I go to gain good background knowledge and learn technical details about Monero?
There's a pretty solid introductory website over at http://moneroinfo.org. I typically point people there if they are completely brand new.
A good place to start would be https://getmonero.org/home, try looking at the various topics under Knowledge Base. If you have further specific questions, you can ask on Reddit, IRC, or here.
Here! Just ask what you would like to know, or browse the other questions. Searching by tags is a useful way to find a lot about a certain topic.
The best information can still be found on the CryptoNote website. (CryptoNote is a cryptocurrency platform from which Monero descends.)
You can find a well-illustrated explanation of the general principles here: https://cryptonote.org/inside/
Low-level technical descriptions/standards can be found here: https://cryptonote.org/standards/
Note that Monero is more and more diverging from this, so not everything will apply directly. The overall principles are the same, though - at least until Confidential Transactions (CT) is deployed in Monero.