You do not need a plastic liner or tarp if you are making an old fashioned backyard ice rink (traditional).
In order to make ice, you simply pack snow, flood the snow surface with water and allow it to freeze.
You can make this traditional backyard ice rink with or without boards.
I recommend building your rink using boards even with a traditional backyard ice rink, especially for those families who want to play hockey.
It is much more fun to play hockey with boards, because the rink boards prevent the puck from flying out of the rink, and your time is spent playing hockey instead of searching for pucks.
When the weather gets consistently cold (colder than -5 degrees Celsius or 23 degrees Fahrenheit) and you get enough snow (anywhere from 20 to 30 centimeters), pack the snow as hard as possible.
You can pack snow by stepping directly on it over and over.
Packing snow is very time consuming and most probably you will need to pack snow more than once at the very beginning when making your old fashioned backyard ice rink, especially when the weather fluctuates.
Get all the family and a few friends to help and make it a fun event! You will need all the help you can get. The more you pack and the tighter the snow gets, the easier time you will have when freezing your surface!
You can also pack snow by placing some plywood boards onto the unpacked snow and stepping on them.
I also recommend that you go over your snow with a basic yard roller in order to pack it tightly and evenly. This is an extra step but it will save you a lot of misery when it is time to flood your snow surface.
If you use a yard roller make sure you fill it with at least 80 pounds of water.