You writeasked,
I hear that chmod 777 is a horrible idea. […] Why shouldn't I allow everything?
and then mentioned in a comment,
I have been having permission issues getting Steam to download games on another filesystem
If it's a Linux-native filesystem you can either change the mount point to your owner, or if you must then set it to be writeable for all users. This second option is not ideal because of the principle of least privilegeprinciple of least privilege: you don't give access unless it's necessary/appropriate. You can't predict what might happen so you don't allow what you don't expect.
Example
# Take ownership sudo chown "$USER" /path/to/mountpoint If you've already downloaded items as root but really should have downloaded them as yourself, use the recursive flag to take ownership of everything under the filesystem mountpoint
sudo chown -R "$USER" /path/to/mountpoint Note that if you try these commands on / or any of the system directories you will break your system.