This page describes the different ways you can multitable and some brief history about each type.
Setup and usage of the StackAndTile application is on the other help pages.
This is the most common layout. Most people are probably already tiling their tables without even knowing the name for it. It is the most intuitive way to arrange your tables.
In this setup, all of your tables are spread out on your screen and visible at all times. Normally, you would place all of your tables side by side, so you have a view of them all simultaneously.
However, the total amount of tables that you can play at the same time is limited to the size of your screen. You can only play so many tables before you have to start overlapping them.
This setup was made popular by the 2+2 post: 24 Tabling Like A Pro
Stacking your tables was a new idea at the time of the above post. The idea is that you put all of your poker tables in the same location on the screen. They would be placed on top of each other. How do you then make your decisions on the tables that are underneath? This setup relies on the fact that the poker site will "Pop up tables when it is your turn to act". Most poker sites have an option for this.
The benefit of this setup is that it allows you to play more tables than would otherwise fit on your screen. Since they are all on top of each other, they do not take up any more space. Another benefit is that all of your decisions are in the same location. You do not need to move your eyes or the mouse all over your screen, because all of your tables are in the same place.
The downsides of this setup are pretty large. Stacking makes it very difficult to remember the previous action of how the hand played out. There is also no way to remember which are 'good tables' and which aren't. What if you are dealt AQ on two tables at the same time? On one table you raise preflop but on another table you call a raise. When these tables are lost at the bottom of the stack, and then pop to the top again, it may be very difficult to remember which AQ is which. Also, all tables are treated the same when stacking, which can be a problem if you have a special heads up table or if you make a final table of a tournament. Finally, you are not able to see other tables that require action that may be of more interest to you.
Stack And Tile combination
Combining the beneficial aspects of the two styles above is the basis for this software app and its name. By including the stacking component, you get to play as many tables as you can handle, without worrying about screen space issues, since all the tables where you are waiting in between hands will be placed in the stack. However, when you decide to play a hand or get an important table, the table will be moved aside, into a tiled grid, allowing you to watch the full hand play out, and not forget the previous action that has taken place. This also allows you to see other tables that require action in the interim.
This style of multitabling was introduced by user "Chiren" on 2+2. He was a worldclass Warcraft player who took up online poker, and started a challenge thread to play 1 millions hands in 1 month. In that thread, he revealed a custom made program that he used to assist him when playing. The video he demonstrated had some bugs, but nevertheless the underlying concept was a revolutionary idea. After seeing his video, I decided to attempt to build a similar program just for fun. People seemed to love it. After thousands of feature requests, bug fixes, and refinements, SaT exists today.
In cascading, the tables are arranged on top of each other with a small offset, aligning diagonally down your screen. Here is an example of what cascading looks like. It has most of the same downsides of stacking, and in addition it also takes up more screen space. However the offset allows you to remember an approximate position of each table, which can assist you in remembering the previous action as the hand plays out.