Going back to a really basic idea, we have 32 bits for our memory addresses. That works out to 2^32 unique combinations of addresses. By convention, each address points to 1 byte of data. Therefore, we can access up to a total 2^32 bytes of data.
In a 32 bit OS, each register stores 32 bits or 4 bytes. 32 bits (1 word) of information are processed per clock cycle. If you want to access a particular 1 byte, conceptually, we can "extract" the individual bytes (e.g. byte 0, byte 1, byte 2, byte 3 etc.) by doing bitwise logical operations.
E.g. to get "dddddddd", take "aaaaaaaabbbbbbbbccccccccdddddddd" and logical AND with "00000000000000000000000011111111".