How would I safely connect 2 sets of 2-3 leds to a nano without using an external power source?

This is my first project. I want to Do it right

What kind of LEDs? For normal LEDs, you can use a resistor per LED and connect that combination to a pin; requires 6 IO pins. You can create grouping in software.

Keep the current through a LED / resistor below 20 mA. There does not seem to be a specification for a group of pins (as for the 328P processor as used in the classic Nano; I'm aware that you did post this in the Nano Every category).

The total current through the Vdd or GND pin of the processor may not exceed 200 mA; 6 x 20 mA equals 120 mA so you're safe.

You can also connect 2 / 3 LEDs (plus resistors) to one pin. In that case you need to use larger resistors so you don't exceed the absolute maximum 40 mA of a pin; it's actually never advised to be close the the maximum and I would limit to 30 mA per pin.

Led strip that was able to be cut down

What kind of LED strip?

5v programmable there is not much info on the roll but it is 5x12mm

A photo of the end of a strip, showing 2 or 3 LEDs, would help us understand what it is you're asking.

Right. So the complication is, each of those white squares contains 3 LEDs, and technically, without knowing exactly which product the white square is, the maximum current per LED is not known - conservatively, I might assume 15 mA per colour. Means each white square might consume 45 mA of power, and if you attached two strips, each with 3 of those, that's ~270 mA of current - if you turned all on full, simultaneously.

This takes only 1 data pin per strip, so 2 pins total. No issue there. However, the 5V regulator on a nano is pretty weak. 270 mA is a fair amount of current, which leads to another question.

What is your power source - USB, or a wall wart plugged into the black connector on the board, and if the latter, what is it's voltage?

The mini usb.

Ahh. Then you have ample power available for what you're proposing to do - just connect the + of the strips to the 5V pin of the Nano, and the GND pin of the Nano to the - of the strips.
While not essential for such a simple, small setup, in larger strip applications you'll see a series resistance (330 ohm, typically) between the data pin of the Arduino and the DIN pin of the strips, and generally, it's a good idea to have that resistor there. There's also typically a large capacitance connected to the power pins of the LED strip; again, unlikely to matter for you with strips this size, but almost essential for larger strips.

Or 2 coin cell batteries if that is feasible.

Nvm

Could i do three of the white squares? Also, could I have visual of the where to connect things I also plan to have a button to change the color of the LEDs.

Here is some info and here also

I’m trying to put this in a prop so idk whether to use cell batteries or just a cord. If someone has a suggestion.

Yes, 2 strips of 3 white squares is quite acceptable.

Have a look at the info linked by @sonofcy , come back with questions. We like to help learners.

Battery is often problematical; we'd have to have a discussion of intensity, duration of use, etc. before we could really be definitive. Larger batteries (e.g. 4-pack of AAA) are more hopeful, but duration of use and intensity are both still factors.

The datasheet will tell you. The approach is to discover how much current each LED will consume, then multiply that by the number of LEDs in the strip. I have seen that go to several AMPS. Now multiply the amperage in milliAmps (Amps * 1000) and multiply that by the number of hours you want them on between charges. If it is larger than roughly 3,000 then you need multiple Lithium batteries. Each battery is cylindrical and measures 18mmD x 65mmL, or goto a LiPo and they are more like a small brick in size and weight.
Do NOT wire Lithium batteries in parallel unless a full BMS is used. You will also need to buy a proper charger, I recommend and use this

No, only one pin is needed! The Dout pin of one strip would be connected to the Din pin of the second strip.

@olivia_ok8 But if wiring like that is inconvenient in your prop, you can use 2 Arduino pins.

I am just going to use the usb. Btw how should I connect the strip to the to the nano to supply power? Basic Connections | Adafruit NeoPixel Überguide | Adafruit Learning System The example you sent talks about an external power I just wanna make sure I get it correct before I start soldering.

Simply connect the button between an Arduino pin and ground. No need for external resistors or any connection to 5V, you can use the Arduino's internal pullup resistors.