How is the hash for a file calculated? Is the file just read bit by bit to calculate the hash with those values or is there more to it?

Are there any resources to read a bit more about file hashing?
Hash functions operate on blocks like SHA-256 has 512-bit input block. In SHA-256, your data $m$ is divided into 512-bits blocks $m_1,\ldots,m_n$ where each entered into the hash function. The final block, $m_n$ is padded as 

$$k=(447−l) \bmod 512$$ where data size is $l$ and $k$ is the number of zeros following the 1 after $m$ and finally the message size in 64 bits. The message size can also 128 which allows larger files to be hashed. So the input to SHA-256 is

$$m\|1\|0\ldots0\|\text{size_of(m)}.$$

Each other hash function defined in a similar way, an example from FRC4634


  The hash functions specified herein are used to compute a message
     digest for a message or data file that is provided as input.  The
     message or data file should be considered to be a bit string.  The
     length of the message is the number of bits in the message (the empty
     message has length 0).  If the number of bits in a message is a
     multiple of 8, for compactness we can represent the message in hex.
     The purpose of message padding is to make the total length of a
     padded message a multiple of 512 for SHA-224 and SHA-256 or a
     multiple of 1024 for SHA-384 and SHA-512.


Note: The 64-bit (or 128-bit) message size also determines the maximum input size for a SHA-256 hash.