First of all, tightvnc is an application which allows you to control your other computer (desktop/laptop) via a network. It's different compared to normal ssh connection, since you will have full access to your desktop, but it's same with SSH X11 Forwarding but with less configuration (IMHO)
OK, let's start the very simple tutorial. Install tightvnc package by issuing installpkg tightvnc-1.3.10-i486-1.txz or slackpkg install tightvnc if you are using slackpkg. This will install a vncserver (server) and vncviewer (client) components.
All you need on the server is to run the vncserver application with some configuration. The most basic configuration is by running
vncserver -geometry 1024x768
this will run the vncserver in background, listening for incoming connection from vncclient and setting the screen as 1024x768 (change this to your resolution). You can view other options by issuing man vncserver. Don't forget to add a strong password so that it will give you extra protection to your computer.
Here's an example:
willysr@desktop:~$ vncserver -geometry 1024x768
You will require a password to access your desktops.
Would you like to enter a view-only password (y/n)? n
New 'X' desktop is desktop:1
Creating default startup script /home/willysr/.vnc/xstartup
Starting applications specified in /home/willysr/.vnc/xstartup
Log file is /home/willysr/.vnc/desktop:1.log
Remember the display part. You will need them to access your server. In this case, it's 1 (desktop:1).
In order to access the computer, run vncviewer and enter the IP address of the computer along with the display number. For example, if other computer is running on 192.168.1.2 and the display number is 1, you entered 192.168.1.2:1. Enter the password that you have set up before and if you are authenticated, you will have full access of your other computer in your current computer.
If you want to have fullscreen access, you can pass -fullscreen into the vncviewer command.
Here's an example of tightvnc in action from Slackware-Current to Ubuntu Lucid Lynx 10.04 Beta 2