Between the ‘big picture’ and the mathematical details, a single-page recap of various keys, addresses, scopes (private/public, spend/view, on-chain/off-chain, payer’s/payee’s) and their relations.
To receive XMR you only need to provide the payer with an @address where they can send funds to. Most of the time it's easier to just share a QR code and let the payer scan it, instead of copy-pasting the alphanumeric string. With the GUI every generated address come with its QR code. Make the person scan the QR code with the Monero @wallet on their phone and receive your XMR in minutes. Remember you can generate as many addresses (subaddresses) as you want. This is useful if you want to keep funds separated for any reason.
To use Monero, the first thing you are going to need is a wallet. Visit our Downloads page and get the right wallet for you. The Monero wallets are available for a variety of platforms and contain everything you need to use Monero immediately.