How do I add bitcoins to a paper wallet? How do I withdraw them?
Treat a paper wallet like a piggy bank: Add funds as often as you like, but only import (or "sweep") your funds once.
How to transfer bitcoins to a paper wallet
Open your live wallet software (e.g. Bitcoin-Qt or Electrum or Mycelium) or web-based wallet (e.g. blockchain.info, coinbase.com) and transfer funds from your live wallet to the public address shown on your paper wallet.
How to withdraw/spend bitcoins using a paper wallet
The way you will access your funds will be to "import" or "sweep" your paper wallet. This effectively transfers the coins from your paper wallet to a live wallet, whether that be electrum, bitcoin-QT, blockchain.info, etc. You should always sweep the complete balance, as it's not safe to try to spend directly from the paper wallet itself.
Virtually any wallet that includes a "import private key" feature will accept the private key hidden under the folds of your paper wallet. However, not 100% of wallets have this feature. Many exchanges and online web services (like Coinbase and blockchain.info) do.
Important note for BIP38-encrypted paper wallets
Not many bitcoin wallet applications or web services are able to directly import BIP38 password-protected private keys. In this case, you will have to use the "Validate" feature on the generator to extract the unencrypted Wallet Import Format (WIF) key as an intermediate step before sweeping the balance.
Blockchain.info has an "Import Private key" feature which supports both regular wallet import format (WIF) and BIP38-encrypted private keys.