Install a graphical environment (X, GUI) & VNC server on your Linux VPS server to connect to it from your computer and use it as a desktop computer:
$ apt-get install xorg
The following NEW packages will be installed:
intel-gpu-tools libfs6 libgl1-mesa-dri libgl1-mesa-glx libglu1-mesa
libpciaccess0 libxcursor1 libxdamage1 libxfixes3 libxi6 libxinerama1
libxkbfile1 libxrandr2 libxtst6 libxv1 libxvmc1 libxxf86dga1 libxxf86vm1
x11-apps x11-session-utils x11-utils x11-xfs-utils x11-xkb-utils
x11-xserver-utils xbitmaps xfonts-100dpi xfonts-75dpi xfonts-base
xfonts-scalable xinit xinput xorg xorg-docs-core xserver-common
xserver-xorg xserver-xorg-core xserver-xorg-input-all
xserver-xorg-input-evdev xserver-xorg-input-mouse
xserver-xorg-input-synaptics xserver-xorg-input-vmmouse
xserver-xorg-input-wacom xserver-xorg-video-all xserver-xorg-video-apm
xserver-xorg-video-ark xserver-xorg-video-ati xserver-xorg-video-chips
xserver-xorg-video-cirrus xserver-xorg-video-fbdev
xserver-xorg-video-i128 xserver-xorg-video-intel
xserver-xorg-video-mach64 xserver-xorg-video-mga
xserver-xorg-video-neomagic xserver-xorg-video-nouveau
xserver-xorg-video-nv xserver-xorg-video-openchrome
xserver-xorg-video-r128 xserver-xorg-video-radeon
xserver-xorg-video-rendition xserver-xorg-video-s3
xserver-xorg-video-s3virge xserver-xorg-video-savage
xserver-xorg-video-siliconmotion xserver-xorg-video-sis
xserver-xorg-video-sisusb xserver-xorg-video-tdfx
xserver-xorg-video-trident xserver-xorg-video-tseng
xserver-xorg-video-v4l xserver-xorg-video-vesa xserver-xorg-video-vmware
xserver-xorg-video-voodoo xterm
0 upgraded, 74 newly installed, 0 to remove and 0 not upgraded.
$ apt-get install xfce4
The following NEW packages will be installed:
aumix aumix-common consolekit dbus dbus-x11 desktop-base
desktop-file-utils exo-utils fortune-mod fortunes-min gconf2
gconf2-common ghostscript gnome-keyring gsfonts gstreamer0.10-alsa
gstreamer0.10-plugins-base gtk2-engines-xfce gvfs gvfs-backends hal
hal-info hicolor-icon-theme hunspell-en-us indicator-application
libappindicator0 libarchive1 libatasmart4 libatk1.0-0 libatk1.0-data
libavahi-client3 libavahi-common-data libavahi-common3 libavahi-glib1
libbluetooth3 libcdio-cdda0 libcdio-paranoia0 libcdio10 libcdparanoia0
libck-connector0 libcroco3 libcups2 libcupsimage2 libdbus-glib-1-2
libdbusmenu-glib1 libdbusmenu-gtk1 libeggdbus-1-0 libenchant1c2a
libexif12 libexo-0.3-0 libexo-common libffi5 libgconf2-4 libgcr0 libgdu0
libglade2-0 libgnome-keyring0 libgp11-0 libgphoto2-2 libgphoto2-port0
libgs8 libgsf-1-114 libgsf-1-common libgstreamer-plugins-base0.10-0
libgstreamer0.10-0 libgtk2.0-0 libgtk2.0-bin libgtk2.0-common
libgudev-1.0-0 libgvfscommon0 libhal-storage1 libhal1 libhunspell-1.2-0
libidl0 libimobiledevice0 libindicator0 libjasper1 libjpeg-progs
libjson-glib-1.0-0 liblcms1 libmagickcore2 libmagickwand2 libnotify1
libntfs10 libogg0 liboil0.3 libopenobex1 liborbit2 libpam-ck-connector
libpam-gnome-keyring libpaper-utils libpaper1 libplist1
libpolkit-agent-1-0 libpolkit-backend-1-0 libpolkit-gobject-1-0
libproxy0 librecode0 librsvg2-2 librsvg2-common libsexy2 libsgutils2-2
libsmbclient libsoup-gnome2.4-1 libsoup2.4-1 libstartup-notification0
libtalloc2 libtheora0 libthunar-vfs-1-2 libtiff4 libusb-1.0-0
libusbmuxd1 libvisual-0.4-0 libvisual-0.4-plugins libvorbis0a
libvorbisenc2 libwbclient0 libwnck-common libwnck22 libx86-1
libxcb-atom1 libxcb-aux0 libxcb-event1 libxcomposite1 libxfce4menu-0.1-0
libxfce4util-bin libxfce4util-common libxfce4util4 libxfcegui4-4
libxfconf-0-2 libxklavier16 libxres1 libxxf86misc1 miscfiles mtools
notification-daemon ntfsprogs obex-data-server orage oss-compat pm-utils
policykit-1 policykit-1-gnome psfontmgr python-dbus python-gobject
radeontool shared-mime-info smartdimmer tango-icon-theme thunar
thunar-data thunar-volman udisks usbmuxd vbetool xdg-user-dirs
xfce-keyboard-shortcuts xfce4 xfce4-appfinder xfce4-mixer xfce4-panel
xfce4-session xfce4-settings xfce4-utils xfconf xfdesktop4
xfdesktop4-data xfwm4 xfwm4-themes xscreensaver xscreensaver-data
0 upgraded, 172 newly installed, 0 to remove and 0 not upgraded.
$ apt-get install vnc4server
The following NEW packages will be installed:
vnc4server xbase-clients
0 upgraded, 2 newly installed, 0 to remove and 0 not upgraded.
$ vncpasswd
$ cat <<'EOF' > ~/.vnc/xstartup
#!/bin/sh
# Uncomment the following two lines for normal desktop:
# unset SESSION\_MANAGER
# exec /etc/X11/xinit/xinitrc
[ -x /etc/vnc/xstartup ] && exec /etc/vnc/xstartup
[ -r \$HOME/.Xresources ] && xrdb \$HOME/.Xresources
xsetroot -solid grey
#vncconfig -iconic &
#x-terminal-emulator -geometry 80x24+10+10 -ls -title "\$VNCDESKTOP Desktop" &
#x-window-manager &
startxfce4 &
EOF
$ vncserver :1 -geometry 1024x768 -depth 16
$ vncserver -kill :1