Below I have posted a photo of how I connected two 9v batteries. Is this the correct arrangement or is there another way? Because I am only getting a 8.55 v read when I connect a wire from each column.

 

You have connected the batteries in parallel so one of your batteries must be flat? Are you after 18V?

 

Yes I am looking to double the voltage to 18v. Do I have to connect them a another way? Both batteries show 8-9v

 

Is there another way I could wire it?

 

You need to connect a black and red wire together away from the breadboard to put the batteries in series. The red and black wire you have left will have 18V across them, these two wires go into the breadboard positive and negative rail.

 

Hey, I got them to produce 18v, thank you very much, I think I learned one of the most elementary lessons in electronics.

 

But now when I add a fixed 12v voltage regulator, the total 15v from the 12v led is reduced to about 3v. How come?

 

How can you get 15V from a 12V LED?? An LED is not a generator.

How did you "add" a 12V regulator to a 18V center-tapped battery??

See, we don't know what you are doing because you never attach your schematic.

 

Here is the schematic that I would like to build on a breadboard. The toggle switch will not mount on the breadboard without ruining the wholes. Any solutions?

 

You should look at the datasheet for the 7812 voltage regulator. Every schematic on it has the important input and output capacitors that are missing on your schematic.
I flipped things around on your schematic so that wires do not cross.

9V batteries are weak even when new. Maybe your fan needs more current than they can supply.
Measure the 18V when the fan is connected to the 7812. If it is low then the batteries are not strong enough to power your fan.

Then measure the output of the 7812. It should be 12V. If it is less than 12V then maybe the fan draws more than the maximum current of 1A from the regulator or if the regulator is too hot and has shut down. If it is hot then it needs a heatsink.
Does the 7812 get hot?

 

Thank you for your revised schematic. It is much more easier to understand. But a couple questions, first how can I tell which pins are which on the regulator and toggle switch(pictured below) i.e positive, ground. And second how can I incorporate the switch onto the breadboard? As they keep damaging the contacts when pushed in.

 

You are supposed to see the datasheet for the regulator to see how to use it and see which pin is which.

You are supposed to use wire that is a certain size on a breadboard.

 

But a couple questions, first how can I tell which pins are which on the regulator and toggle switch(pictured below) i.e positive, ground. And second how can I incorporate the switch onto the breadboard? As they keep damaging the contacts when pushed in.

Look at the datasheet for the regulator.

For the switch, solder some wires (22 or 24 AWG) onto the switch pins, and plug the wires into the breadboard. If you use stranded wire, you will need to tin the exposed ends in order to insert them into the breadboard.

In SPDT toggle switches, the center pin is the wiper and the two outer pins are the other contacts. The switch connects the wiper to one of other contacts, namely the one that the toggle is not pointing toward. In the attached photo, the wiper (with the yellow wire) is connected to the pin with the green wire. ETA: You could have figured this out with a DMM.

Also attached is a photo of the way I connect two 9-volt batteries in series on a solderless breadboard. In this way, you have access to the outputs of both batteries individually, or both in series.