I have a public and private key written down. If i want to import that to bitcoin qt, do i simply go to addresses->New address, and then type in the public key?
Nope, you need the private key instead.
Click Help -> Debug window -> Console, and enter importprivkey <bitcoinprivkey>
Alternatively, if I want to create a new wallet, do I go to receive->new addresses and then create one there?
If you want to create a new
receiving address, yes.
If you want to create a new
wallet, close you bitcoin-qt, rename your wallet.dat to something else, and then open your bitcoin-qt again.
If I want to send from that address, do I simply then copy that address and then go to addresses and then new address and copy and paste that new address into the address box?
Nope, the address tab is for you to store the addresses you have
sent bitcoin to (such as a gambling site or an exchange).