sending money to germany?

Does that person need to use dollars? Maybe to pay a debt in the USA?  If not then surely it would be better for that person to have euros, to spend in Germany.

Do it through PayPal. 

The easiest way to send it would be PayPal. It can be deposited into their bank account. I suppose they could then go to a currency exchange office and change it into dollars, although that seems like a very strange thing to do. 

If what you want is for the person to receive $1000 in US cash, you can't except if you send cash. That is generally considered a bad idea, though it's not illegal. Cash sent by mail has a pretty good chance of going missing.

I'm not sure why you want someone in Germany to receive US currency. If what you want is to be sure they get exactly that amount, you can write a cheque that says '1000 USD' or you can send the equivalent in euros with a cheque or money order, or have your bank transfer it to their bank.

I will point out that it is illegal to mail US currency - this coming straight from a Fedex guy's lips some years back. So you can do it but if it is found it will be confiscated.

Cash? my guess is send paper currency - although the euros can be converted top USD at a bank.

It will only be paid out in Euros, even if you send as USD. It can be exchanged  back, if it makes any sense to do so.

You could shove it into an envelope and send it through mail or courier.