How can I remove unwanted app icons from the screen? I'm new to using an android.  Apps I have never visited nor installed are showing up on my screen (Slots, Candy Crush, Expedia, Droid Games).  If I touch them, I go to their site.  I would like to remove them but can't figure out how?  Any ideas?
Sounds like you tapped into some spam trap. Certain apps place advertisements this way -- though the new playstore rules do no longer allow that. Others do the same in the notification area. Airpush is the best known evil source of such.

I suggest you scan your device for such apps. Try e.g. with TrustGo Ad Detector. Quoting from the apps description:


  It is common for advertising networks to collect information on how you use your device. Your information is then used for targeted marketing campaigns.
  
  Some common and aggressive methods include:
  
  
  Pushing ads to your Android notification bar
  Creating unauthorized shortcuts on your home screen
  Modifying the default browser, homepage and bookmarks settings
  Subscribing you to emails and text messages when an ad is clicked
  Making phone calls and downloading malicious files when an ad is clicked
  


At least one line sounding familiar? (remark: emphazation is mine).

EDIT: Once you've identified the malicious app, make sure to...


report it to Google (according to the current playstore rules, this kind of advertisement is not permitted)
comment on the app to warn off other users
uninstall the app and leave it out
think about whether in the future you want to use any apps from such developers which do not respect your privacy
nothing bad with ad-financed apps -- but it a) should be clear where those ads come from, and b) they should be related to the app itself, i.e. being displayed in that app when it's used -- and not outside in different places whether you use the app or not