I understand the scriptSig and scriptPubKey mostly now. What happens in a transaction is A private key goes through the process of ultimately proving that the address the BTC was "sent" to matches. This initially "signs" it but then it must be verified with the public-key. The public-key then also verifies the signature and provides further evidence that the signature is valid. This is now open to go to the scriptPubKey portion of the script that ultimatly just specifies which address is the recipient of the BTC or signature. Within the output is also the quantity sent. Then when this is received by the new owner they have to go through the same input process, prove possession of the address storing the value, etc., etc., thus the system acts as a series of electronic signatures.

Looking at the necessary things for the input portion of a transaction, I see that they are 1) the previous tx 2) the index and 3) the scriptSig. I understand the scriptSig now(In a basic way I believe) and the index, which just refers to the specific output of the tx in question. I don't understand however how the "previous tx" represents the previous transaction(sounds strange but let me explain). Does the previous tx represent a hash of the finished signature of the previous tx? And how is this used as an essential part of the input.

I have a few little theories. Maybe the "previous tx" section of an input is just a hash of the referenced output address? Again, maybe it's just a hash of the previous tx signature? But then, I think, scriptPubKey only gives the output address. If scriptPubKey gives more than just the output address I think it would explain this last piece of the puzzle and I'd understand the basics of the script process. My impression is that scriptPubKey just contains the value and the output address.