I hope it is a free website (non Blogspot, wordpress.com sort of addresses). If so, follow the steps mentioned below:

1. Ensure you have an email address on your domain name (i.e. not gmail.com, yahoo.com,etc. addresses)

2. Click here to visit the website downtime monitoring service

3. Choose to opt for a Free trial

4. Enter your website details in the application form. Please note: Free email addresses (eg: gmail, yahoo, hotmail,etc.) are NOT allowed. Also, Enter a proper domain name (i.e. no .blogspot.com URL)

5. Enter all the details and then press "Sign up"

6. Check your email address and Verify the account. 

Your website will now be monitored for free. However, do note that if you have more than one website, you will have to pay a nominal fee per month to monitor your website uptime.