chown to change ownership and
chmod to change rights.
As Paweł Karpiński said, use the -R option to apply the rights for all files inside of a directory too.
Note that both these commands just work for directories too. The -R option makes them also change the permissions for all files and directories inside of the directory.
sudo chown -R username:group directory
will change ownership (both user and group) of all files and directories inside of
sudo chown username:group directory
will only change the permission of the folder
directory but will leave the files and folders inside the directory alone.
As enzotib mentioned, you need to use
sudo to change the ownership from root to yourself.