What exactly do I send?
You can find what is an ethereum transaction in this answer. This is what you are sending.
what am I signing?
The transaction before signing will include everything except
v, r and s. These are generated from the signature. This function can explain in more detail.
what do I do to my signed transaction?
Your signed transaction will be send to a node. This could be a node run by you or one that you access via an API(e.g. Infura). The nodes will propagate this transaction to every other nodes that they are in touch with. You can read how state transition happens and how transactions are handled here