It's very simple.
For User:
chown username filename
chown username directoryname
Recursively:
chown -R username directoryname
For Group:
chgrp groupname filename
chgrp groupname directoryname
Recursively:
chgrp -R groupname directoryname
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Change groupname and username at the same time.
chown username:groupname filename
Change username and groupname at the same time recursively.
chown -R username:groupname directoryname