What are the parts of a Bitcoin Transaction "Input" script? All the terminologies I find seem rather confusing about what explains what and they usually miss a few steps.  

Example: Transaction 82d62d5f4e69ae8338c39b7ae2e1d33db59bdf62c869ded7344adc936bab8653

Found at https://blockchain.info/tx/82d62d5f4e69ae8338c39b7ae2e1d33db59bdf62c869ded7344adc936bab8653

Shows an "Input Script" of:

3045022100d52330113ccd033ccb1aaa3b759e9696c216e802922e5f1902cd5ada69c612e5022057880205319dccb05eebbe34323a852ee82653f09f81253ddccd08a810e9d42d01
03e5b9f0bb669b289efb8d2826487a24ef5f3985624c8bc3a3e34f6bd54e080b27

So, what parts of that are what, and how can I tell which parts are what in this transaction's "input script" as well as others?
3045022100d52330113ccd033ccb1aaa3b759e9696c216e802922e5f1902cd5ada69c612e5022057880205319dccb05eebbe34323a852ee82653f09f81253ddccd08a810e9d42d01


Is a DER encoded ECDSA signature. I'll break it down:


  30


indicates that a compound structure follows (ECDSA signatures are treated as a compound of 2 integers, r and s)


  45


is the total length of the compound structure (excluding the 2 header bytes, 30 45), 69.


  02


the start of the contents of the compound structure, 02 indicates an integer (the signature's r value)


  21


of 33 bytes


  00d52330113ccd033ccb1aaa3b759e9696c216e802922e5f1902cd5ada69c612e5


the integer's value encoded in 33 big-endian bytes. The first byte is zero, as without it, it would be interpreted as a negative number (see 2's complement notation).


  02


another integer follows (s)


  20


of 32 bytes


  57880205319dccb05eebbe34323a852ee82653f09f81253ddccd08a810e9d42d


the 32 bytes encoding the s value


  01


this is a sighash byte appended by Bitcoin, and is not technically part of the ECDSA signature. As such, it's not counted as part of the length 69 (byte 45) at the start. It indicates what fields of the transaction are signed. 01 means "all".