Parallels Plesk is a comprehensive control panel solution used by leading hosting providers worldwide for shared, virtual and dedicated hosting, including us The control panel is designed to simplify the management and administration of web sites. Plesk control panel automates a large number of tasks that allow service providers to reduce operating costs and resources while at the same time increasing profitability, efficiency and customer satisfaction.

Here are the complete steps on "How to install Plesk 8.x on a plain VPS Hosting / Dedicated server"..

Important Pre-Installation Tasks :

Login to the VPS Hosting/server & execute "uname -i" to get the OS bit version so that you can download the appropriate installer package.
[root@server ~]# uname -i
x86_64
Later on, run "cat /etc/redhat-release" to check the name & version of the OS installed on the system, for downloading the appropriate installer package.
[root@server ~]# cat /etc/redhat-release
CentOS release 5.2 (Final)
Run the following 3 commands, to check if Apache, PHP & MySQL are preinstalled by the OS:
[root@server ~]# rpm -qa | grep -i http
[root@server ~]# rpm -qa | grep -i php
[root@server ~]# rpm -qa | grep -i cyrus
[root@server ~]# rpm -qa | grep -i mysql
If the above are found to be installed [most of the time they are] by the OS, they conflict with the applications Plesk installs, hence remove them using...
[root@server ~]# yum remove http*
[root@server ~]# yum remove php*
[root@server ~]# yum remove cyrus*
[root@server ~]# yum remove mysql*
Check SELinux status, we have it disabled but still... execute "getenforce" it should say "Disabled" or "Not enforcing". If it's enforcing, disable it by executing: "setenforce 0".
root@server [~]# getenforce
Disabled
Change your working directory to where you want to download the Auto-installer utility:
[root@server ~]# mkdir /root/plesk
[root@server ~]# cd /root/plesk
Once done, download the Auto-installer utility that suits your operating system from HERE and save it on your server's hard drive.
eg : [root@server plesk]# wget plesk_auto_installer_file_name
Set the execution permission for Auto-installer:
eg : [root@server plesk]# chmod +x plesk_auto_installer_file_name
Run the Auto-installer:
eg : [root@server plesk]# ./plesk_auto_installer_file_name
Read installation notes displayed on the screen and type 'n' to proceed to the next screen. Press ENTER.

Select the product versions that you want to install: type the number corresponding to the product version you need and press ENTER, then type 'n' and press ENTER to continue. Here's a sample of installing Plesk control panel 8.4 on CentOS 5.x
1. [*] Plesk Control Panel
then the following product versions which are available are displayed:
5. (*) Plesk 8.4.0
Select the components that you wish to install by selecting the installation type for Plesk Control Panel.

By default, typical installation is selected. It includes a minimal number of packages required for Plesk to work. To install all components of Plesk including all Plesk modules and Web applications, select Full installation. To install only selected components, select Custom installation. In this screen, choose the proper installation type and press ENTER.
Select the third [Custom] option by entering 3 & press ENTER.
3. (*) Custom
Custom components selection. Recommended only for experienced users.
* To review the components that will be installed, type L and then press ENTER. The selected packages are marked with [*] symbols.
To select or deselect a package, type the corresponding number and press ENTER.

When there are several versions of a component available for installing, for example, PHP v. 4 and PHP v.5, then you can choose the version that you want to install..

Primary components list for Plesk control panel. Select the components of Plesk Control Panel you want to install:
Show components for the product:

1. (*) Plesk Control Panel
2. * Base packages of Plesk
3. [*] Plesk Updater
4. [ ] PHP5 support
5. [*] PosgreSQL server support
6. [ ] Application vault packages
7. [ ] Additional Plesk manuals
8. [ ] Plesk Professional Web Web site hosting Editor
9. [*] Plesk API [former Plesk Agent]
10. [ ] Plesk migration manager
11. [ ] SiteBuilder publishing support for Plesk
12. [ ] SiteBuilder module migration suite
13. [ ] ColdFusion support for Plesk
14. [ ] MIVA Empresa support
15. [ ] <+> Plesk hosting features // 0 of 6 components selected
16. [ ] <+> Additional Plesk modules // 0 of 5 components selected
17. [ ] <+> Game servers // 0 of 3 components selected
18. [.] <+> Addition mail services // 2 of 5 components selected
19. [ ] <+> Server backup solutions // 0 of 1 components selected
20. [ ] <+> Additional language packs // 0 of 8 components selected
1, 2, 3, 4, 5, 6, 8, 9, 10, 15, 16, 18 & 19 should only be selected.

Make sure that only the following components are selected & the page should look like:
1. (*) Plesk Control Panel

Please select the components of Plesk Control Panel you want to install:
2. * Base packages of Plesk
3. [*] Plesk Updater
4. [*] PHP5 support
5. [*] PosgreSQL server support
6. [*] Application vault packages
7. [ ] Additional Plesk manuals
8. [*] Plesk Professional Web Web site hosting Editor
9. [*] Plesk API [former Plesk Agent]
10. [*] Plesk migration manager
11. [ ] SiteBuilder publishing support for Plesk
12. [ ] SiteBuilder module migration suite
13. [ ] ColdFusion support for Plesk
14. [ ] MIVA Empresa support
15. [*] <+> Plesk hosting features // 6 of 6 components selected
16. [*] <+> Additional Plesk modules // 5 of 5 components selected
17. [ ] <+> Game servers // 0 of 3 components selected
18. [.] <+> Addition mail services // 4 of 5 components selected
19. [*] <+> Server backup solutions // 1 of 1 components selected
20. [ ] <+> Additional language packs // 0 of 8 components selected
15, 16, 18 & 19 have sub-components & they need to be selected too:
15. [*] <+> Plesk hosting features // 6 of 6 components selected
16. [*] <+> Additional Plesk modules // 5 of 5 components selected
18. [.] <+> Addition mail services // 4 of 5 components selected
19. [*] <+> Server backup solutions // 1 of 1 components selected
15. [*] <+> Plesk hosting features // 6 of 6 components selected
1. [*] Bandwidth Limiter For Apache support (mod_bw)
2. [*] Apache ASP support
3. [*] Tomcat Java Servlets support
4. [*] Apache mod_python module
5. [*] Ruby on Rails support
6. [*] FastCGI support (mod_fcgid)
16. [*] <+> Additional Plesk modules // 5 of 5 components selected
1. [*] Plesk Firewall module
2. [*] Plesk VPN module
3. [*] Plesk Fileserver module and SMB file server package
4. [*] SSHTerm - SSH Terminal java applet
5. [*] Watchdog (System monitoring module)
18. [.] <+> Addition mail services // 4 of 5 components selected
1. [*] Mailman mailing list manager support
2. [ ] Kaspersky antivirus module
3. [*] Dr. Web antivirus
4. [*] SpamAssassin support
5. [*] Real-time Blackhole List client for qmail
19. [*] <+> Server backup solutions // 1 of 1 components selected
1. [*] Plesk Backup Manager
To continue with installation, type 'n' and press ENTER. When prompted, confirm installing: type 'n' and press ENTER again.

The packages will be downloaded and installed automatically. Hence you can get yourself a cup of coffee in the meantime
When the installation is finished a trial license key is installed for evaluation purposes & Plesk will have started automatically..
Now to complete the initial configuration, log in to the Plesk control panel running on your host:
https://hostname.domain.name:8443/
https://ip-address:8443/
Use the username 'admin' and password 'setup' (both are case sensitive). For security reasons, change the password upon initial login..

Enjoy going through the control panel.. I'm sure you'd like it...