How do I go about creating an authorization group?

This all depends. In some cases authorization groups must exist in a custom table before they can be used. This is true for table authorization groups (authorization group in table TBRG assigned to tables in table TDDAT via transaction SE54) and user groups (created in transaction SUGR). In some cases authorization groups are merely created when they are assigned to the object in a standard maintenance transaction (e.g. vendor master data, customer master data, material master data etc.) In other cases the authorization group has an optional validation table that is used in search helps but no where else (ABAP programs in table TPGP and TPGPT, report writer authorization groups (via table TBRG) etc. Authorization groups are essentially labels that you assign to objects (tables, programs, master data etc.) that allow authorization checks for access to the objects with the label.