How can I use my XRP paper wallet private key (or "private address") to send XRP to another address? I know that once a private key touches the internet, the wallet can't be used again (for security reasons). So, the only time when I'll be importing my key is when spending the funds. I have a simple XRP private key (it is not encrypted or anything) that starts with letter "s".
The phrase “paper wallet” is a slightly overblown name for a sheet of paper with one-or-more cryptographic private keys on it. At its simplest, a “paper wallet” could be handwritten on the back of an envelope. It may have optional extra information, such as a public address derived from the private key. For XRP, a public address begins with “r”. Ideally, for maximum security, the private keys would be generated on a computer that's not connected to the internet.
Your example has a string of letters & numbers beginning with “s”, commonly known as a ripple secret, but more properly called a family seed. For brevity, I will call it a seed.
A software wallet can convert this seed into a private key (and also a public address). If you enter the seed into a software wallet on an internet-connected computer, you will have a hot wallet. But you obviously care about security (since you're holding a paper wallet…), so perhaps you would prefer a cold wallet. Here are two examples of wallet software that works in both hot and cold modes (don't try them until you've read the rest of this answer):—
They may look like so-called ‘web wallets’, but they do all of their cryptography inside your browser. So, you can enhance your security by downloading the pages and running them directly on your computer. For true cold wallet functionality, transfer them to a computer that's not connected to the internet. The Bithomp wallet is newer & more intuitive, but RipplemRM's wallet has some interesting bells & whistles.
“But Wait!” I hear you exclaim. “How can I spend my XRPs from a cold wallet if it's cut off from the internet?” The answer is to pair it with a view-only wallet. Enter your ripple address (beginning with “r”) into either of the above wallets, but not your seed (beginning with “s”), and you will have a view-only wallet. With a view-only wallet, it's impossible to lose your funds by accident, but you can draw up an unsigned transaction. The wallet uses the internet to consult the XRP ledger and make sure your transaction is properly formed, but it's not valid without a signature. If you want the transaction to happen for real, you have to transfer it (as a file on a USB stick?) to your cold wallet. Your cold wallet is exactly the same software as your read-only wallet, except
It's running on a disconnected computer
You enter your seed into it (safe since there's no internet connection).
Your cold wallet can add a cryptographic signature to your unsigned transaction file. Then you can transfer it back (USB stick again?) to your view-only wallet and tell the view-only wallet to broadcast it over the internet. The XRP network will validate the signature against the originating address (thank to the magic of asymmetric cryptography, it does this without knowing your private key), and your transaction will be recorded forever on the XRP ledger.
Alternatively, if you like living dangerously, you can just use a hot wallet (enter your seed into wallet software on an internet-connected computer; but if using the Bithomp or RippleRM wallets it's still a good idea to run them from downloaded copies). The wallet itself will not leak your private keys if you downloaded the genuine wallet, but malware on your computer is still a risk.
You will find the BitHomp wallet easier to use (both hot and cold modes), but it's worth knowing that the RippleRM wallet starts up with a demo account (the seed is snoPBrXtMeMyMHUVTgbuqAfg1SUTb), which can be useful for learning. I guess you could try out the same demo account in both. Also, the RippleRM wallet is denominated in drops (1 XRP = 1 million drops). With either wallet, be careful not to accidentally unset your address's master private key unless you can live with the consequences.
If you had a hexadecimal private key rather than a seed, you could use it in RippleRM's wallet. If you had a mnemonic phrase rather than a seed, you could use it in the Bithomp wallet.
If you opt for cold signing, remember that malicious USB sticks are sometime planted in places where they get picked up & used by gullible people. Finally, you should not cut-&-paste the above links, because I'm a random stranger on the internet. Type them out by hand in case I'm a thief trying my luck with an IDN homograph attack.
EDIT: Here's another reason for using cold signing. Active XRP accounts hold a reserve of 20 XRPs, so if you abandon an account because you don't trust the private key, you're throwing away $6.54 at today's exchange-rate.