Quote from: shardison25 on October 03, 2018, 01:47:40 PM

I save my address(es) and use the address as payment?

You don't explicitly use addresses for payment. On a technical level addresses don't exist.

What you actually do (or better: your wallet does) is, taking multiple UTXO and combining them to new UTXO's.
A part of these new UTXO's (usually one) is being assigned to the receipent, while another UTXO is being assigned to a new address of yours (your change).

To do this your wallet does need to sign the transaction using the private keys associated to the UTXO's you want to use.

So, all you need to keep care of are the private keys. In modern wallets (almost everyone, including electrum) you only have to backup a 12 or 24 word mnemonic code.
All of your private keys (and therefore also public keys + addresses) can be derived using this word phrase (keep multiple backups AND secured + hidden from curious eyes).

Quote from: shardison25 on October 03, 2018, 01:47:40 PM

can someone send me a link to a intro to bitcoins?

I'd suggest visiting bitcoin.org. You'll find basic information there.
For further interest, google does give you quite a lot useful results.