thank you for starting this topic!
First off, under normal circumstance (not much connected to the Arduino) a simple 2A 5V USB power-supply, for example from your phone, or a cheap one from AliExpress, eBay of Amazon, would do the trick. The 5V feed from the USB port of a computer is is sufficient as well - as seen when programming the Arduino.
If however, you need to power something that is power hungry, for example a LED strip, then a stronger power-supply is recommended.
Here we would see two scenario's;
1) The Arduino is still connected to a PC.
This can be in scenario's where you are still developing, or when the PC provides the Arduino with data (see the Boblight
project for an example).
In this case the LED strips need to be powered separately, since neither Arduino nor PC can really handle this much load on their pin's or USB port.
It is important that +5V does not get mixed though, as seen in the figure 4 of the Arduino and WS2812 article
2) The Arduino is not connected to a PC.
In this case, the power supply for the extra components (LED strips for example) can be used to power the Arduino. See figure 5 of the Arduino and WS2812 article
Now we do want to be careful with this of course - in the depicted example the power-supply is 5V regulated, so that will work.
If however your power-supply is not 5V (9V or higher) then the extra connector can be. But ... be careful here as well, the regulator can handle on so much, so make sure you wire things correctly and do not try to pull 5B through your Arduino from, say a 9V power-supply, to feed the LED strips.
In the end: learning a little about electronics is recommended if you decide to connect more components to your Arduino.