Shell Programming and Scripting

Hello,
I have been given a scripting project, but have not learned any scripting. I need to get some ideas on how to start. Attached is part of the project:

I have no idea how to parse the arguments. What I had in mind was to get the arguments ($1, $2, ... ) and have if statements for different cases. The different cases are:
1-argument --> pid
2-arguments --> (-g pid, pid -g, -n name, name -n, -gn name, -ng name, name -gn, name -ng)
3-arguments --> (name -n -g, name -g -n, ...)

but this clearly isn't the right way to do it.
Here is the usage variable btw:

USAGE='Usage: KillByName.sh [-g] -n <name> or KillByName [-g] <pid>'

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