how to connect external monitor to macbook pro?

Have been using external monitor with MacBook pro for several years now. Use Vizio 24" monitor with hdmi cable and converter. Recently the desktop on monitor has not been complete. the background image appears, sometimes the menu bar, sometimes the dock at bottom. However non or the icons on desktop now appear. Can sometime open applications and icons on the monitor but not always. Never had problem like this before.

I connected a Vizio 19" monitor, everything works fine, but in switching back and forth encounter issue with larger monitor described above.. I can scroll with pointer from built in screen to 24" monitor, and drag icons over, but they don't stay. it's as if there are two different screens that don't match up..

I have been through system preferences on MacBook, reviewed every screen setting on Vizio but unable to regain full access to desktop on monitor. It is likely a setting of some type, but I can't figure out what it is!

Any suggestions??

thanks,

Bill