Yes, the permissions should be 644 and 755 as explained by Shyam, but the other posters forget to mention that this is if the file is owned by your webserver, and the group is the group you belong to.
For instance, in FileZilla you will see permissions something like this:
Filename Size Filetype Last Modified Permissions Owner/Group
somefile.txt 11KB txt file 2014-04-23 3:43:00 AM www-data myGroup
The permissions drwxr-xr-x are 755 (just ignore the leading dr so it's wxr-xr-x). Read permissions are worth 4, Write permissions are worth 2 and execute permissions are worth 1.. so having them all add up to 7, and that's what the owner of this file has. The group has read and execute permissions but not write, so they have 5, and everyone also has 5.. making the permissions 755.
754 would be owners having read, write, execute. Group having read and execute, and everyone only having read permissions.
In the example above, you can see that the file owner is www-data (which is the default web server group for many Apache servers) and the Group is the group myGroup, which is the Group (admins) that I belong to.
The first number is the owners permissions, the second is the groups' permissions, and the third number is everyone's permissions. Obviously, you have to be careful to give the web server the permissions it needs... and make sure the files that need to be locked down can't be written or executed by just anyone (the third number).
Below is what the numbers mean:
Assuming the Webserver owns the files, your admin is in the group, and of course, everyone is the third number.
644: Files with permissions set to 644 are readable by everyone and writeable only by the file/folder owner.
755: Files with permissions set to 755 are readable and executable by everyone, but only writeable by the file/folder owner.
777: Files with permissions set to 777 are readable, writeable, and executable by everyone. Don’t use this set of permissions, for security reasons, on your web server unless absolutely necessary, and only temporarily. It's a disaster waiting to happen, especially if a directory has those permissions.. it means anyone can upload files and execute them.
Here are the Linux commands to setup the Joomla! recommended permissions from the command line. Recommended Joomla File Permissions
Set ownership: sudo chown -R www-data:myName /path/to/your/domain.com
Set Directories: sudo find /path/to/your/domain.com -type d -exec chmod 755 {} \;
Set files : sudo find /path/to/your/domain.com -type f -exec chmod 644 {} \;
NOTE - many people will show you these commands without the path, but I prefer to ALWAYS use the complete path, because if you forget to change directories to the root Joomla! installation directory and run them without the path, you have just changed permissions for every file and directory in that top directory, and created a huge mess.
After you run these commands, you will need to fix permissions for any directories that need more permissions... for instance...users uploading images etc.
IF YOU ONLY USE THE JOOMLA! interface, and you don't have admin or FTP access to the server, then USE THE OWNERSHIP and PERMISSIONS ABOVE.
STOP HERE IF YOU ARE A NOVICE.. the Below is only for people that truly understand what permissions and ownership do.
However, I find having the ownership and permissions that way very unhandy because I like to use FileZilla and a Terminal session command line most of the time, and I upload a lot of files manually. But I can't overwrite any files because I don't own them and I don't have permissions to write. I could have FileZilla log in under the web server account, BUT... I want FileZilla to log in under my account, so I can browse other directories also, not just the files the webserver has access to... SO... I change the ownership and permissions to this:
Filename Size Filetype Last Modified Permissions Owner/Group
somefile.txt 11KB txt file 2014-04-23 3:43:00 AM drwxr-xr-x myName www-data
I make myself the owner, and put the web server in the Group... and I change the permissions for directories to 775, and for files to 664. Makes my life a lot easier... but I don't recommend it for everyone.
If you do it my way, these are the commands:
Set ownership: sudo chown -R myName:www-data /path/to/your/domain.com
Set Directories: sudo find /path/to/your/domain.com -type d -exec chmod 775 {} \;
Set files : sudo find /path/to/your/domain.com -type f -exec chmod 664 {} \;