This is based on my experience with a Raspberry pi 3 running Raspbian Jessie.

Setup SSH
 
In Raspbian Jessie ssh may already be enabled by default but if not open a terminal and type
sudo raspi-config
select 7 Advanced Options
select A4 SSH
You’ll be asked if you want enable SSH Select Yes.
To find the IP address of you pi open a terminal and type:
hostname -I
On another computer open terminal(Linux) or command line in Windows, I’m using Ubuntu and type;
ssh pi@<YOUR Raspberry Pi IP ADDRESS>
It will prompt you for your password. NOTE: the default password for the user pi is raspberry, you can now change this.
 
Now install VNC Server on the Raspberry pi
Open Terminal, and type:
sudo apt-get install tightvncserver
To start VNC Server, type:
tightvncserver
You’ll be asked to set a password to access the pi. You’ll need this when you try to access the pi from another computer.
To run VNCServer at Startup
You will normally want the VNC Server to run automatically after the Raspberry Pi reboots, open a terminal and type:
cd /home/pi
cd .config
mkdir autostart
cd autostart
Create a new autostart file for TightVNC by typing the following:
sudo leafpad tightvnc.desktop
This will open the default text editor (leafpad) with a blank file called tightvnc.desktop Edit the contents of the file with the following text:
[Desktop Entry]
Type=Application
Name=TightVNC
Exec=vncserver :1
StartupNotify=false
Connecting to Raspberry Pi via VNC
 
On another PC open Remina (or other VNC Client)
server address is IP-Address-of-Your-pi:1 (note :1 which defines display 1)
Username is pi
Password is: whatever you set for Tightvnc
You should now have a VNC connection to your pi.
This is all fine if you want to run the pi headless and administer it remotely but, if like me you want to run a pi with a monitor attached as a display sign for example then you will need to be able to display the same monitor output on both HDMI and VNC. Remember from above the pi was displaying session :0 and VNC displayed session :1
To achieve this I used X11VNC rather than TightVNC
 
Install X11VNC
Open a Terminal and type:
sudo apt-get install x11vnc
x11vnc -storepasswd
As with TighVNC before we need to set X11VNC to autostart in a terminal type:
cd /home/pi
cd .config
mkdir autostart [You can miss this step if you’ve already created the directory]
cd autostart
sudo leafpad x11vnc.desktop
Type the following text into the x11vnc.desktop file:
[Desktop Entry]
Encoding=UTF-8
Type=Application
Name=X11VNC
Comment=
Exec=x11vnc -forever -usepw -display :0 -ultrafilexfer
StartupNotify=false
Terminal=false
Hidden=false

Note: If you created an autostart file for TightVNC as above, then remember to either remove this file from the autostart directory or delete it, otherwise when you reboot your pi it will try and start both TightVNC and X11VNC.

You should now be able to connect to your Raspberry pi using your VNC client with the IP address of your pi (without the :1) and it should display the same output as the Rasperry pi HDMI monitor.