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I want to log in to my new installed RHEL 6.2
I tried to log in with root, and password that I created during the installation process, but after log in this appears root@myName ~1# : what should I write? I wrote startx but it didn't work

My initial reading is that you were expecting a graphical environment. Correct me if I'm wrong. Either way, you're looking at the command prompt and can start using the system however you were wanting to use it as long as you're OK with command line.

From the bit about startx not working, it sounds like you installed a basic server during the initial install. Starting with RHEL6 this doesn't install a GUI. You can approach this three ways:

1. "Meh It's a server anyways. All I need is command line."


2. Since it's a new install, start over again, but pick an installation profile that's likely to install a GUI.


3. 
   

   Manually install the GUI components and manually start/configure the X server. If you're brand new, I'd say that if you go with this option this is easiest path:

   
   
   
   
   
   • Install Xorg via yum groupinstall "X Window System"
     
   
   
   • Install GNOME (my preference, you can do KDE if you want) via yum groupinstall Desktop
     
   
   
   • Switch to the graphical mode (runlevel 5) via telinit 5
     
   
   
   • 
     

     Once in, open /etc/inittab (you can use gedit or something like that, you may have to yum install gedit to get the editor, though) and ensure the default run level (what the system boots to automatically) is set to 5:

     
     
     

     id:5:initdefault:
     
     

     
     
   
   

   • If you're really paranoid, you can check the above with a reboot command.

   
   
   
   

EDIT:

I should note that the above assumes that you're already registered with RHN, otherwise you don't have yum repos to install the above from (well, you do, but the process of installing from the DVD is probably too complicated for new users). If you're uncomfortable with doing the rhn_register in order to do the registration (which is a guided TUI so it's not hard to use if you're using hosted and not Satellite, which I'm going to take a wild guess and assume you're not doing) then a reinstall is probably the best case.

Really depends on what your comfort level with the various options is.

What precisely is your goal? If it was just to log in as root, you did do that and you have access to the system, but it sounds like you might be wanting a graphical login instead of the command line.

If that's your goal, then you'll need to make sure that you have X and a desktop installed, then switch your default runlevel to 5.

Section 35.3 lists the steps: https://access.redhat.com/site/documentation/en-US/Red_Hat_Enterprise_Linux/6/html/Installation_Guide/sn-switching-to-gui-login.html

Edit:
The linked doc also has the steps for using your installation DVD as a repository, but as Joel mentioned, it is probably less complicated as a new user to do a re-install with the desktop packages installed from the get-go.