just write a narrative of the diagram following the numbers. I've never tried this, here goes
1. from the blockchain, a transactions public key is mashed together with a random number
2. a specific output is used
3. bobs private key is used
4. the above three things are mashed together into a private key
5. another random number mashes with a public key
6. number 5 gets mashed with the following
and I got lost and im at work and peeps gettin coffee.
Well, no, that's not really how it works. 
1. For the sender, a random transaction private key is chosen.
2. The sender does a ECDH with this private key and the receiver's public view key.
3. From that derivation and an output index, he is able to use the receiver's public spend key to create a one-time output public key for which only the receiver will be able to generate a private key.
To generate this private key:
1. The receiver does an ECDH with his private view key and the public transaction key (from tx extra)
2. From this derivation (which matches exactly that from step 2 above), the receiver does the same as step 3 above.
3. If his result matches, he knows he owns the output. He can then use his private spend key to generate the corresponding output private key (to actually spend the output).
I figured as much, but that was my point - the diagram is not very helpful for those of us that are all like "my compooter gone did done some mafs"
Thank you though! - the above is short and sweet, but dnaelor's actually matched up with the diagram numbers. And yes, one of those "floating hand draws and some guy talks" animation things would be cool
Yes, I was only covering the stealth address portion, which, IMO, is harder to "get" than the ring signature portion. dnaleor's covers the full transaction, but also isn't quite correct.
The graphic doesn't really explain stealth addresses at all, so the first part of this is basically inline, but I've added a bit to it anyway.
let me give it a try
Bob wants to spend XMR he received in his account and send it to Carol.
How does he compose the transaction?
A: Bob gets acces to his "real input" that was send to his "stealth address"
1. Bob needs the public key from the transaction that contains the output he received and wants to send
- Bob needs to ECDH this key with his private view key2. Bob also selects the exact number of the output from the transaction that contains the output he wants to send. The other output(s) in this transaction is/are change (Bob doesn't have the private key for those other outputs)
Note: typically, due to auto-denomination, Bob will have more than one output per transaction that belongs to him.3. Bob needs the "master" private key of his account
- private spend key, to be precise4. 1,2 and 3 are used to calculate the private key for the specific output he wants to send. (the public key for the transaction can be calculated from this private key
- This is correct, but the public key is also stored on the blockchain.)
B: to protects Carol's identity, Bob will do the folowing to generate a "one time" public key for this transaction, making it impossible for others to link all transactions send to Carol to the same "stealth address"
5. Bob generates a random
number scalar, this one isn't clear from the graphic at all6. this random number is
hashed into the transaction public key the transaction private key, and is scalar mult'd into the transaction public key
7. he selects the number associated with the output
s (due to auto-denom) that Carol will receive, the other output(s) is/are change that goes back to Bob.
8. he needs the "master" public key from Carol to be able to send it to her stealth address
- Carol's public view key9. 6,7 and 8 are used to calulate the public key for the specific output
s he wants to send
C: to "mix" the inputs, Bob creates a ring signature
10. He selects the actual public key
(+ that output's private key) from the output he wants to send, but he also adds other public keys into the mix.
11. to prevent double spending, Bob needs to send a valid "key image" together with the public keys of the outputs
(or inputs if you prefer).
12. he signs the combination of inputs and the key image with his private key, prooving the key image is valid (Bob owns the private key associated with the key image) and that (somehow? I don't know how this works) one of the public keys is used to generate this key image, but as a spectator of the blockchain, we can't know which of the used outputs is "the real one that is being transferred".
His private key and the other chosen public key(s) are used to create a ring signature; they'll be one signature for each input, collectively making a ring signature. The key image is an additional public key computed from the output private key (not public key) that's actually being spent.13. This is the collection of outputs that is signed. He grabbed the "fake ones" from the blockchain. He doesn't need permission from the owners for that.
This isn't quite right: those are the outputs that are doing the signing. A hash of the TX prefix is "what" is actually being signed.14. This is the key image he signed. If Bob ever tries to send the same output again, the exact same key image will be generated and thus the double spend will be detected.
15. this "ring signature" is added to the transaction containing the publi keys that are used in the transaction and proving Bob's ownership of one of those inputs.
tell me if I was terribly wrong
edit: damn it, luigiiii is faster than me
