My website doesn't work at www.domain.tld, only domain.tld?

Plesk does not automatically set up www.domain.com for you. You will have to enable it as follows:

Linux
If you have tried to manually set up DNS records for www.your-domainname-here.tld in the DNS Settings please remove these before proceeding

Under:
Domains > your-domainname-here.tld > Domain Administrator
You can enable the WWW record here.

Windows
If you have already added a domain to your VPS then there is no option to enable the WWW record afterwards. You will need to add the WWW host header by hand:

First you will need to create a DNS record for www.domain.tld to point as a CNAME to domain.tld under:
Domains > your-domainname-here.tld > DNS Settings > Add Record

Connect to the VPS through Remote Desktop and then load up the IIS Manager:

# Start > Run > type inetmgr and press enter
# Under the websites folder find domain.tld, right-click on it and do to 'Properties'.
# Under the 'Web Site' tab click the 'advanced' button to the right of the IP address field

In here click 'Add' and the values you need are:
# IP Address: the IP address of your VPS
# TCP Port: 80
# Host Header Value: www.your-domainname-here.tld

To set this up automatically for any new domains you add to your Windows Plesk VPS go to (in Plesk):
# Server >> DNS Settings >> Add new record
# The record you are adding has to have the following details:
Record Type: CNAME
Domain name: www
Canonical name: <domain>

Note: actually use <domain>, do not replace this with your domain name or anything.