Note: Make sure you check the important notes below the instructions.

These are the instructions from Plesk's manual.

To allow anonymous FTP access:
1 Click the Anonymous FTP icon in the Hosting group.
2 To activate anonymous FTP service, click the Switch On icon.
3 To set up a welcoming message to be displayed when users log in to
FTP site, select the Display login message check box and type the
message text in the input field as desired.
Note that not all FTP clients display welcoming messages.
4 To allow visitors to upload files to the /incoming directory, select the
Allow uploading to incoming directory check box.
5 To allow users to create subdirectories in the /incoming directory,
select the Allow creation of directories in the incoming directory check box.
6 To allow downloading files from the /incoming directory, select the
Allow downloading from the incoming directory checkbox.
7 To limit the amount of disk space that can be occupied by uploaded
files, deselect the Unlimited check box corresponding to the Limit disk
space in the incoming directory option, and specify the amount in kilobytes.
This is the hard quota: the users will not be able to add more files to the directory
when the limit is reached.
8 To limit the number of simultaneous connections to the anonymous
FTP server, deselect the Unlimited check box corresponding to the Limit
number of simultaneous connections option and specify the number of
allowed connections.
9 To limit the bandwidth for anonymous FTP connections, deselect the
Unlimited check box corresponding to the Limit download bandwidth for this
virtual FTP domain option and enter the maximum bandwidth in kilobytes
per second.
10 Click OK.

Important Notes:
There are 2 requirements for the anonymous FTP icon to show up for your domain.
1) the domain setup must be using physical hosting and
2) configured on exclusive IP only
3) When you change the IP it may take from 4h-24h.
During that time plesk will probably show the default host's page.
A nice workaround for this is to create an .htaccess file in
/var/www/vhosts/default/htdocs/

This snippet will proxy the requests to your domain from the default one.
That way you won't have to wait.

RewriteEngine On
RewriteOptions Inherit
Options -Indexes +FollowSymlinks +Includes

RewriteCond %{HTTP_HOST} ^(www\.)?example\.com$
RewriteRule .? http://example\.com%{REQUEST_URI} [P,L]

Users should be able to log into ftp://example.com using user: anonymous and any password.