First, some information is required. What directory are you trying to create your files and directories in? If it's your home directory (/home/$USER where $USER is your user name) then you should have full permission to do this. Anywhere else on the system you need root permissions.
What distro are you using? If Ubuntu root is disabled, and you get root permissions for individual commands by using sudo -- by default you are listed in the file /etc/sudoers. Other distros have sudo, which is a good way to run root commands, but you have to, as root, enter your own name into /etc/sudoers, usually by using visudo.
Assuming this is your own system, and you've simply lost or forgotten the root password, you can always use a live cd. Take either your installation disk (Which I assume is a live cd) or Knoppix, open a terminal and type "sudo su". This is the workaround even for Ubuntu for getting root permissions. Then do a "mkdir harddrive", find the name of your Linux installation by doing an "ls /dev/hd*" and you should be able to work it out, type "mount /dev/hd? harddrive" where the ? is the letter or letter number combination (hda1 for example) do a "cd harddrive" and, having checked with ls to see your directory reads something like:
bin dev lost+found opt sbin sys var
boot etc media proc selinux tmp cdrom home lib mnt root srv usr
(which is what I got from my root directory) do a "chroot ." Notice the period after chroot. That is, change the root path to this directory. Now type "passwd root", and make something up. Then type exit, reboot, log into your regular system, open a terminal and type "su". It will ask you for root's password (on knoppix typing sudo su will have it ask for yurs. Just type enter: there is no password). Enter root's password and you will have root's permissions for all commands entered in that window. Write the password down, if you must, and/or enter your user name into /etc/sudoers if it is not there and sudo will work in the latter case including sudo passwd root.
Of course if this is a shared system, and I learned Linux commands on a shared system at college as a user, not an administrator, then forget all this. Talk to administrators and/or ONLY create files and directories in your home directory. If it is your personal computer, though, the workarounds I mentioned should work.