Once you have installed PsyScript, open the 'readme.html' file you find in that folder. You should be able to double-click that file to make your computer open it in your favourite web browser. If this doesn't work correctly for you, consult whoever set up your computer. Once the PsyScript editor is open you can use it like any other web page: bookmark it, find it in your History menu, etc..
To do anything useful with PsyScript you need a folder with two files in it. On the PsyScript editor page you will see a link which lets you download a blank project folder. You will also find this folder in the PsyScript folder.
When you do the last step you should see the text under the icon change to the name you've given the file, and the contents show in the big text field. If it did that, everything worked and you're ready to start using your new project folder.
From now on you normally make changes to the script text by typing in the editing window rather than manually changing what's in the text file. Unfortunately it is not possible for a web browser to save changes to your script file by updating the script file on your disk. You will have to do it yourself.
PsyScript remembers what script file you're working on and what's in it, but you will want to save a copy of the script for use safe storage, or for use on another computer, or for when you need to switch from one script to another. So when you want to save your changes …
If you like to work that way, it's safe to keep the text file open the whole time you're working on your script in the PsyScript editor, just occasionally copying your changes back into the file and hitting 'Save'.