Electrum were designed to be user friendly when compared to full wallets, not sure why you don't full understand it features.
"how to use Electrum to make a payment"
Go to send tab, Input destination address, amount, description [Optional], and then set your Network Fee.
Just press send and input your password, and your transaction will appear both on Blockchain and your History for easy Book keeping.
"how to use Electrum to receive a deposit".
Go to receive tab and give your address to the person or website you'd like to receive your coin from.
I see for my receive transaction I have a "transaction id", one "input" hex number and two "output" hex numbers. When would I want to know them and then how to use them to do what?
Transaction ID are used as a proof that you have sent your coins to the recipients, think of it as a receipt.
You can either right clock on your transaction and press "View on Block Explorer" or copy its hex and paste it into Block Explorer Manually.