If you run a GTK-based desktop environment on your Raspberry Pi, getting remote desktop working with Vino is extremely easy.
Step 1: install the package:
sudo apt-get install vino
Step 2: Configure the server to not prompt to allow connections and use an empty password:
gsettings set org.gnome.Vino prompt-enabled false
gsettings set org.gnome.Vino vnc-password ''
Step 3: Start the server:
systemctl --user start vino-server
Now you can connect using any VNC capable client.