Yes, figure out roughly how much power you pixels will need. 30 neopixels all set to white at full brightness will need close to 2A. That's the most it would ever need. Using a lower brightness and colors closer to red, green, or blue will reduce it. While LEDs aren't all that linear with brightness, 10% brightness could be close to 200mA. Of course if only a subset of the pixels are ever lit, then power requirements are going to be proportionally less.
The cap is a good idea to mitigate the potential current demand surge when the strip gets power. However, with such a small strip it's not imperative.
To connect:
The data input to the strip always connects to your controller board. Ground always connects to ground. ALL grounds need to be connected together. Power is connected to power of your controller if you're not using an external supply. That limits you to a few 100 mA for the pixels. If you need more, you'll need an exteral supply. In which case the strip power connects to the +ive from the power supply, and as before, ALL grounds connect together.
In the pack you got, both black wires from the strip are ground (and are connected already on the strip), red is power, and white is data in.
You will need to solder in some way to connect to the supplied wires. It's a skill well worth having. See
https://learn.adafruit.com/adafruit-guide-excellent-soldering for a good soldering tutorial.
Dave