DVD Shrink does not burn - it rips, encodes and compresses only. You need a third party program such as DVD Decrypter or Nero in order to burn. If you have one of these installed, you can then tick a option in DVD Shrink to have it use one of these programs to burn.
Have a look at http://www.dvdshrink.info it has guides on how to use DVD Shrink. DVD Shrink uses DVD Decrypter to burn when you select it. You don't need to run DVD Decrypter yourself, just have it installed. Adder.
when I go to back-up on DVD shrink....it does not have the option for me to burn under "select backup target" it says to instal nero and I have....how do I get it to burn
In DVD Shrinks settings tick the box that says 'Enable burning with Nero'. So when DVD shrink has finished what it has to do it will then ask you to put the blank media into your writer and off it will go. Make sure if you have just installed Nero to restart your computer before using it.
Decrypter will only burn in ISO mode. You will need to use the ISO Read and ISO Write functions. If you movie is larger that 4464Mb you will need to run it through DVD Shrink in order to fit on standard single layer DVD.