But I hear a lot about how a wallet has both private and public keys, where the private keys are what send money.
Can someone please clarify this? ;-;
Bitcoin addresses use asymetric Public-key cryptography. For each address you create, there is a secret matching part that is stored in your wallet, but is never shown to you. The secret key is used for digitally signing messages transferring your bitcoins to someone else when you want to send a payment, to prove that you authorized the transfer.
This is merely an interesting fact. To receive a payment, just give someone your address. To send a payment, just put in their address and the amount to send, and press "send coins".
Your knowledge is sexy, my friend.