Are you using a third party launcher, like Nova Launcher, or anything? If you are try uninstalling it and rebooting the phone. If you dialer returns you can try to install it again.
If you aren't using a launcher, other than a native one installed on the phone when you bought it, touch the phone icon and when it brings up People or Contacts, look at the top of the screen just above the list of people. Are there other selections there? For me to the right of People is Groups but to the left is Favorites, Phone and Call History. Try swiping Left and see if that takes you to your dialer.