This isn't really special to Logic.
See links like this
http://guides.macrumors.com/UninstallingApplications_in_Mac_OSX
or
http://www.thexlab.com/faqs/uninstallingapps.html
However this is just basic googling. When you run the application itself it will write our preference files and possibly create other subfolders (for instance Logic when installed will put the loops and samples in the default music/apple loops folder), also if you install additions to an app (such as a plug in or perhaps have more loops or instruments to add, you have to know where they are in order to truly clean things out).
Generally it's enough to simply close the app, drag it to the trash and delete it.
However a lot of software companies will deliberately created 'hidden' files or obscure some config files simply to stop things like evaluation software from being reinstalled over and over. So that when you think you have uninstalled the software and then try to install it again, the machine 'knows' that the expiry date or 'number of tries' has been exceeded.
Generally looking at my simply logic set up I would go for
1) Drag the Logic Express app from the applications folder to the trash.
2) Drag the apple loops folder from the music folder to the trash
3) Drag [username]/library/preferences/com.apple.logic.express* files (I have two, a 'cs' and a 'plist' file) to the trash. There is a library dir for each user (depending on how you have your mac set up - you may have more than one location of logic installed, but you will only have the preferneces in the 'users' own library dir).
4) If you are comfortable with CLI you can open a terminal
then type
su -
hit return
when prompted enter the root password, this will give you enough permissions to search the whole disk rather than as the user you are logged in as.
then type
cd /
hit return
Then type
find / -name "
logic"
and hit return
This will cause a search for any file with the word 'logic' in its name and list them. Be patient this will search the whole disk. When it has completed you can scroll through the list and see the full path to the files.
Note: This doesn't mean every file that is reported has anything to do with Logic, so use some common sense.
When the search is finished then you will see the prompt again. Remember you are still logged in as 'root' in the terminal, so close the Terminal app or press ctrl-c to log out of the terminal session and back as your normal user. I don't want to be blamed for screwing up your mac because you went roaming about in terminal as root. 😉
Also, just because it won't hurt, I'd reboot once you had emptied the trash.
As I say, this isn't gospel and if anyone else can offer any other advice I'd be more than interested to hear it.
TTFN
P