Quote from: SurReality89 on February 27, 2015, 07:38:33 PM

can i just see an example. like how do you get from the private key 1 to the public key and then the address.

Sorry, I'm not going to sit here and type up all the math for you. I've explained the concept, and given you some resources.

Quote from: SurReality89 on February 27, 2015, 07:38:33 PM

also when you have the private key and public key/address where do you go to transfer to another public key/address?

You use wallet software. You tell the software what address you want to send the bitcoins to, and how much you want to send. The wallet takes care of the rest.

The wallet creates a sequence of bytes of data representing a transaction that is supplied value by listing some previously unspent transaction outputs and then assigns that value to new unspent outputs. Proof that you have the right to spend the previously unspent outputs is supplied by the wallet software by using the private key to calculate a digital signature of a modified version of the transaction. This signature can be verified by all nodes on the system by using the public key.

The new outputs include a script that place a requirement that must be met in order for any node to accept that output being used as an input. The most common requirement is a digital signature from a private key that is associated with a particular public key hash. This is represented with an "bitcoin address" when presenting the interface to the user.