chmod 777 filename

owner rwx
group rwx
other rwx

chmod 7777 filename

4000 - Set the effective User ID
2000 - Set the effective Group ID
1000 - Set the sticky bit

So a file of 7777 means:
a file which is read-writable-executable by all, and has its setuid, groupuid and sticky bits set.

chmod u+x filename

add execute permission on file to owner

u - owner
g - group
o - others
a - all

chmod ug=rw filename

chmod ug+r filename

chmod o-w filename