You have everything connected WRONG:
1) The negative black wire from a battery or power supply connects to the purple wire that wrongly connects to the OUTPUT pin of the regulator. But it is supposed to connect to the ground wire of the circuit.

2) The capacitor marked "102" is only 0.001uF(1000pF or 1nF) which is also much too small. It has both of its wires wrongly shorted together at the input pin of the regulator. One of its wires is supposed to connect to the ground wire of the circuit.

3) The ground pin of the regulator and one wire of the output capacitor is the ground wire of the circuit but they wrongly do not connect to anything. They are supposed to connect to the negative black wire from the input power supply and to the ground wire of the output load.

What is the other red wire and the black wire for? The red wire connects to the input pin of the regulator and the black wire connects to the output pin of the regulator so they connect to the input power supply.

 

Why don't you connect everything like is shown on the schematic?

 

So I'm supposed two have two ground wires negative wires coming from the power supply? And the other red and black wires are from the 12v cpu fan I am trying to power with two 9v batteries. I have attached some pictures of the revised circuit. Could you please tell me what is missing. Thank you very much for your patience.

 

So I'm supposed two have two ground wires negative wires coming from the power supply?

No.
All ground wires are supposed to be connected together.
The input power supply ground wire, the circuit ground wire (the common pin of the regulator, one wire of the input capacitor and one wire of the output capacitor) and the output ground wire are all connected together on my schematic. Didn't you see it?

And the other red and black wires are from the 12v cpu fan I am trying to power with two 9v batteries.

Why are you trying to power the fan from the 18V battery? Don't you want to power the fan from the 12V output of the regulator?
1) You wrongly show the fan connected to the 18V battery.

I have attached some pictures of the revised circuit. Could you please tell me what is missing.

2) Why do you have a new capacitor with the tiny value of only 0.000047uF (47pF)?
Why does it wrongly have both wires connected to the output of the regulator instead of having one wire connected to ground like on the schematic?

3) Why do you have another capacitor with a tiny value of only 0.00022uF (220pF)?
Why does it wrongly have both wires connected to ground instead of having one wire connected to the input like on the schematic?

4) Why do you have two purple wires that short the output of the regulator to ground?

 

I have connected two positive wires to the input and output of the regulator. Each with one wire from a capacitor that connects to ground. Finally I have connected one negative wire to the ground pin with the other wire of the capacitors placed here.

 

Good, you have the capacitors connected correctly.
Good, you have all the grounds connected together correctly.

But the capacitors have wrong values.
Why do you have a red wire that shorts the output of the regulator to its input?

 

I cannot find the correct values of capacitors I only have these:221, 473, 101,102k, 10 and 104m. When you say shorted what do you mean? Should I connect this wire to an another power source, or somehow connect it to the original series.

 

Please learn about how Oriental capacitors are marked.
221 is 220pF, 473 is 0.047uF, 101 is 100pf, 102 is 1000pF, 10 is 10pF and 104 is 0.1uF.
J is 5%, K is 10% and M is 20% tolerance.

Shorted means directly connected together. You shorted the input to the output means you directly connected the input to the output. Remove that red wire.

 

Could you briefly explain to me the purpose of the capacitors in this circuit and how you calculated the amount of uf for the input and output?

 

Here's the datasheet

Read it.

 

I use the datasheet of the uA78xx from Texas Instruments.