I'm not an expert, but a couple things to suggest-
Ok, I assume you've downloaded the file from the website- it should say PlaneShift-v0.5.7.dmg, then you've clicked that and it expands into a white hard drive-looking icon that just says PlaneShift, and inside is a folder that says PlaneShift. You need to drag that entire folder into your main Applications folder (the one that looks like an 'A' made out of pencils when you open a new finder window)
Now, the client probably needs updating, so you'll need to run 'pslaunch' which is the updater. If you're still getting a permissions error, then try to change the permissions of both 'psclient' and 'pslaunch.' To do that, right-click on each and select 'get info.' At the bottom of the box it should say 'sharing and permissions.' Open that, and switch the privilege of both yourself and admin to 'read and write.'
If that still doesn't work, try turning every application off, and opening "Disk Utility" (which is found inside Utilities inside the Applications). Click on your hard drive at the left, then click 'repair disk permissions.' That will reset all permissions to what the computer thinks should be the correct settings.
You may need to re-open the 'get info' for 'pslaunch' and 'psclient' and repeat setting the permissions there.
If none of that helps... then sorry, you'll have to ask someone more knowledgable.
Good luck!