Check out the read me file inside the folder you downloaded to your pc.
Heres what it says for the install:
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INSTALL:
BACKUP ALL OF YOUR FILES that you will be overwriting as well as your Database before installing!!!
Run the sql statement (shipdate.sql) in your database - If you do not have the "zen" prefix in your database tables, remove it from the SQL statement before executing it.
Make sure to change any folders labeled YOUR_TEMPLATE to the template you are using.
Copy files to your install.
To change blocked out dates, open the following file and read the instructions contained within it: includes/modules/pages/checkout_shipping/jscript_calendar_head.php
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Check your database for a prefix on your tables if you can't remember if you have one. You can access your database to take a peek from your hosting control panel.
To install the sql patch from your admin panel click Tools-->Install SQL Patches. You can either browse for the deliverydate.sql and upload the file or you can copy and paste (by opening the .sql file with a text editor) its contents into the box then hit send. Heres what the file contains: ALTER TABLE zen_orders ADD order_delivery_date date AFTER ip_address;
Remove the zen_ if your database tables have no zen_ prefix. If they have a different prefix like store_ etc then just replace the zen_ with whatever prefix your tables have.
Now you'll need to upload (ftp) the files to your server. Make sure you you change the two folders named YOUR_TEMPLATE to whatever (custom) template you are using. If you have not yet set up a custom template please do so and check out these articles to get started: How do I create a new Custom Template? , The Override System really simplified