And one end comes with a positive and negative wire attached. I have stripped about an inch from both ends revealing some VERY small stranded wires, and I was wondering how I should go about connecting them into a breadboard because they are very flimsy.
Get a little piece of solid wire and solder it onto the end of the stranded to make a little pin for it. When I trim the leads off of resistors I tend to save the little pieces for just such an occasion.
Cut the lead off a resistor or header pin and wrap the stranded wire around it as tight as possible and cover with tape or heat shrink tubing. It won’t be 100% reliable, but it will work on a breadboard.
The cheapest soldering irons are really cheap. They aren’t much good at much, but they are fine for this kind of thing.
I use a wire ferrule like this (16 ga): https://www.digikey.com/product-detail/en/american-electrical-inc/121210150/288-1096-ND/266462
Wrap the fine stranded wire tightly around a piece of bare 22 ga solid or DuPont header post with the plastic spacer removed, slip the ferrule over the wound part leaving 6 - 8 mm exposed to go in the breadboard and crimp. If you don't have a crimping tool you can use a (preferably dull) pair of side cutters (GENTLY, just crimp, don't cut) then solder if you have the equipment, but it works OK without.
Define small. 2A is not small in my vocabulary
Agreed. 2A is pushing it for a breadboard. Try to spread the current load over 2 breadboard strips if you can find a way to do that, including the ground/0V. Or maybe just limit the pwm values to max 128, assuming you are using pwm.