You don't need to understand everything in the data sheet to use the part. Just pick out the information you need.
Usually a linear regulator requires a "bypass" capacitor connected from the input pin to ground or battery negative. Another one is also required on the output pin to ground. Not all regulators require these capacitors. Sometimes they are only recommended for stability. Other times they are required under all conditions. It depends on the make and part number of the linear regulator. For the TI part, the input capacitor is required. The output capacitor is optional, but recommended for stability. Just about any type of capacitor can be used. Typically, they would be electrolytic. These capacitors are normally polarized which means they can only be connected one way, negative or ground is usually marked on them. This is unlike ceramic capacitors that can be hooked up either way.
Resistors are required to form a "voltage divider" on the adjustment pin. This provides a means to set output voltage. For non-variable voltage, you can pick a reasonable value for one of the resistors (like 10kΩ) and use the formula they give in the data sheet to find the value of the other one. For variable voltage, one of the resistors is a potentiometer or variable resistor. Calculations are more involved, but you can still use the formula to find the range of resistance you need.
The CT pin is the shutdown and timing control for the regulator. However, it's better to use a higher current momentary switch on battery positive. Regulators still draw a small current when shut down. That way, the
mod won't drain the battery at all when idle. However, if you really want to use a low current switch, you can utilize the CT pin for that.
One complication with this part is the need for an additional timing capacitor connected between the CT pin and ground, but that's only for capacitive loading and atomizers are not capacitive. You can probably just leave it out. With a switch on battery positive, you might be able to leave that pin disconnected altogether.
Another complication is how the CT pin works for shutdown (if you want to use that function). It has to "float" for the regulator to be on and pulled to ground for the regulator to be off. You pretty much have to use a transistor or the hard-to-find "normally closed" momentary switch. Not the simplest regulator to use for that. There are better choices like the
NCP630A.
Generally, it helps to understand the basics of how circuits work.
These guys have the best tutorials I've come across on the net. Well written and designed for someone starting from ground zero.