How to send bitcoins by email? How would you send bitcoins to a person by email supposing my bitcoins are stored locally on my machine?

The email is supposely not seen be any other person than the reciever (by using GPG for instance).
You can but you have to use American wallet provider Coinbase but than you have to register and login into their website.

For clarification, your bitcoins are not stored locally on your machine, they are stored on the Bitcoin network which means they are also on my computer and on every other peer's computer. The difference is, you have the access to your bitcoins (you own the private key) and I don't.