Okay now I have this tzedaka box sitting in my living room and it's full of coins and crumpled bills. How do I give that to my favorite charity? Or any charity?
I call Colel Chabad. They send someone to my door with a bag for me to pour all the money in. A few weeks later I get a receipt in the mail for my donation.
Take the coins to coinstar, and they'll count it and donate it all (no fee) to your choice of a handful of major charities. None of them are specifically Jewish charities, but that's okay.
Take the bills to the bank, and write a check correspondingly.
About the bills:
Total up the bills. Mail a check to your favorite charity for the amount, then move the bills to your wallet. Later on, the charity will send you a tax receipt.
About the coins:
Dump all the coins into a charity box outside your home. Charities are good at handling large amounts of coins.
If the coins total more than $20, try to hand them directly to a charity employee or gabbai. Unfortunately, some people steal money from charities, including on erev Purim and erev Yom Kippur when there are dozens of collection pans set out on one table.
Tell the charity that you don't need a tax receipt for the coins.