How to get dark colors on paper through pencil colors?
In the drawing of the hummingbird you posted, darker colored pencils are being used. Children's sets usually have bright, basic colors.

However, you may have some luck getting darker colors by layering what you have. Read up on color theory and combine colors to give the illusion of overall darker hues. The section on tints &amp; shades from the wiki article is particularly helpful, and includes reasoning as to why you should avoid darkening colors with black or lightening them with white:


  It is common among some painters to darken a paint color by adding
  black paint—producing colors called shades—or lighten a color by
  adding white—producing colors called tints. However it is not always
  the best way for representational painting, as an unfortunate result
  is for colors to also shift in hue. [...] Lightening a
  color by adding white can cause a shift towards blue when mixed with
  reds and oranges. Another practice when darkening a color is to use
  its opposite, or complementary, color (e.g. purplish-red added to
  yellowish-green) in order to neutralize it without a shift in hue, and
  darken it if the additive color is darker than the parent color.