If I want to send someone $20 worth of monero and the transaction fee is $10, does that person only get $10 or the full $20 and I pay the $10, so I would end up paying $30 for a $20 transaction?
Thanks,
You would end up paying the transaction fee.
In every cryptocurrency I know of the sender submits the amount they want to the send to the network PLUS the fee they want to spend. The receiver gets the amount you wanted to send and the miner of your block takes the fee you put up, provided it is high enough.
So yes, if you send $20 of monero with a 10$ fee, you'll end up $30 poorer.