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I tried to make a circuit, but the LED is still on even when the push down switch is turned off. I have attached some pictures.
Please tell me what to do. I come from an artistic background. I am trying to make a tiny cosplay pendant that I can sell, so please tell me if I have bought the right material, too. What kind of micro battery cell holder do I need for the two cells?
the LED is still on even when the push down switch is turned off
That one is easy: some of the pins on the bottom of the switch are always connected together. Use a multimeter "beeper" - or just the LED! - to figure out which pair works as you want it to. There will be at least one such pin pair.
The coin cells you're using have maximum of about 20Ω of internal resistance at room temperature, typically 1/3rd of that. Each cell acts as if it was an "ideal" cell with a 5Ω..20Ω series resistor added to it. That's why the LED didn't burn up as it would had you tried it with let's say two D cells and a red LED.
Since the (presumably) white LED has a fairly high forward voltage drop - above 2V - and can sustain high operating currents (>20mA) - there may be no need for an additional series resistor. Due to the cells' small size, though, you want the LED to be running at a low current - about 1mA maximum to have any reasonable cell life, and ideally less.
Thus it may make some sense to add a 220Ω..1kΩ series resistor anyway, just to make the cells last longer than a few minutes. Thus:
simulate this circuit – Schematic created using CircuitLab
The smaller the cell, the lower brightness the LED should be operated at so it doesn't kill the cell prematurely - the lower the operating current it can take to extract most of the energy out of it. To lower the operating current, the series resistor's value need to be increased.
A reasonable range of series resistor values for a pair of LR44 batteries in series working with a white LED is up to 4kΩ or so. Above 4k&ohml the LED is not bright enough, and the batteries are operating well below their rated discharge current.
To be able to exploit the full rated capacity of those tiny cells, the discharge current has to be quite small, but making it much smaller than that gives not much improvement in longevity. The series limiting resistor may need to be above 1kΩ.
If you can measure the current, adjust the resistor so that the current is about 0.2mA. With discharge current at or below 0.2mA, the LR44 battery should achieve its rated 100mAh capacity. Currents above 0.2mA make the battery less efficient and wastes more energy as heat inside the battery instead of light :)
There are lots of questions and answers about lighting LEDs on the site.
Lighting an LED in the hardware world is comparable to printing "Hello World" in the software world (a first beginner project). As such, you should definitely check out some tutorials and other questions first that may clear up some of your confusion.
To more directly answer your questions:
...please tell me if I have bought the right material...
For a costume or "wearable" light, keeping things small and lightweight are usually of utmost importance. A couple of coin cell batteries like the LR44s you have is definitely in keeping to that principle, however they are really designed to power things like watches, hearing aids, and other low-power devices. Since you mentioned "pendant," I assume you want the batteries to be extremely small and housed in the pendant along with the LED.
The LED you've selected appears to be a high-brightness (and high-power) one, which will be far too demanding of the batteries you've selected. So you have an engineering decision to make:
Do you want ridiculous brightness for a wearable that really shines? You'll have to increase your power supply (bigger batteries!) and probably have to run some small wires from somewhere on the person to the pendant. You may also have to consider how hot the LED will get over time and ensure that it doesn't fail from too much heat or even burn the person wearing the pendant.
Do you want the batteries you've chosen to power an LED for a reasonable duration? You'll have to decrease your LED power demands (smaller LED!) and settle for less brightness. But not to worry, you can get quite a bit of brightness from very small, less power-hungry LEDs. For your purposes, consider something like the Adafruit LED "sequins", which are surface-mount LEDs on a tiny PCB that is aimed at making wearable electronics.
Once you've made this decision, you can then fine-tune some things. With a given LED, you can control its brightness by changing the current through it. The easiest way to do that is with a current-limiting resistor (see above list of questions). More current will mean a brighter LED, but also drain the battery faster. Less current will mean less light, but give you longer running time. You'll have to figure out for whatever LED you choose how bright you want it for your requirements of brightness and battery life.
What kind of micro battery cell holder do I need for the two cells?
Electronics vendors sell "battery holders" which can be used to connect cells together and/or attach them to a circuit board, etc. Your cells are LR44 which have a diameter of 11.6 mm. Searching two popular US distributors, Mouser and Digikey, you will discover that most holders for this size of cell are designed only for one cell. There is, for example, a Keystone 501 holder that holds two 12 mm cells, but you would need to use BR1212, CR1216, CL1220, or CR1225 cells.
You will need to do your own research to find specific parts. Manufacturers come and go, parts get discontinued or new parts come into existence, so asking on this site for specific recommendations for parts is off-topic. However, you are more than welcome to ask about a specific part in how to connect or use it, and whether your circuit will operate as expected.
Since the OP asked if they have purchased the right materials for a circuit, that opens up the more general question of selection of LED, switch, battery, and battery holder, as well as supporting circuitry. I'll make some basic suggestions, but specifics will require more detailed specifications.
So, I would suggest that the OP provide a "wish list" of desired performance, and then more specific designs could be proposed and discussed. That should be asked in a separate question.
