When you get the zip file downloaded, you might (depending exactly one what system you use) just click on it to extract it. Otherwise you might have to use a zip extractor.
Now you should have a directory called something like Walnut-main.
Go into that directory and there is a command called "build.sh".
Execute that command - on my Unix system you type
./build.sh
to do that.
That should take a few seconds to compile.
Then go to the "bin" directory and type
./walnut.sh
that gets you into Walnut. To leave, type quit;
You may want to edit the walnut.sh file. If you are running on a machine with more RAM, you can adjust the upper limit of memory usage as indicated in the comment.
For older versions of Walnut, you would have to type
java Main.Prover
or (for Walnut 1) java Main.prover
to get it to start running.
Depending on your system, you may need a "Java Development Kit" to install Walnut. If so, try the command
sudo apt install openjdk-11-jdk
from a terminal window. Once that is done, to compile Walnut, go to the Walnut directory and type
sh build-sh (Windows)
It might be that you can get by without the "sh" before the command, depending on your system.
Or
./build-sh (Linux)
If you are using Walnut under the Eclipse environment, here are a few tips. Download the Walnut software. Start Eclipse up. Use the default workspace. Open "Project" from the File choices, and choose "Walnut". Next, go to src/Main in the menu choices, right-click on prover.java or Prover.java and choose "Run As Java Application". You should now get a window where you can enter Walnut commands. To see results, go to the Eclipse file menu, right-click on "Result" and choose "Refresh" and the results should be there. Thanks to Stepan Holub for this info.
Let us know if you have any difficulties.