I'm new to the ExpressionEngine but I cannot find 'Design' tab in the main menu. Does anyone know how to add it or the provide the sample URL so that I can reach Design page on my site?
First, just to check, you are logged into the Control Panel (where the menu is)? Are you logged in as the super user or another user? Is the user a member of the same group as user 1?
If not, this will indicate user group permissions. The "Can Access Control Panel" permission only allows you in, in the same section there is a "Can access DESIGN section" permission, make sure this is set to yes.
Other permissions to check are in the "Control Panel Administration" section, "Can administrate template groups and templates" and "Can administrate design preferences", Test with these set to yes (these should control what is available in menu).
Finally, check the "Template Editing Privileges" section, this shouldn't stop the menu appearing but again might remove links and if a menu has no links it may not show.
If its not Group Permissions, check your "Main Menu Manager" Settings in "My Account" (Click your name in the top right). See if there's anything going on here.
Finally, check you have no extensions or otherwise 'mucking about' wit hthe menu.
Please check the above, and report back if you don't get any results and we'll investigate further. There's no chance of any tom foolary in the database or core files is there?