As I decided to use LaTeX to make a presentation and I'm a newbie, I would like a not-very-long tutorial that introduces all features of the beamer class package one can use along with its output. Is there any other package which is preferred over beamer?
As Andrew has already pointed out, you can find a good tutorial in the Beamer User Guide, accessible e.g. on http://www.ctan.org/pkg/beamer under the link "Package Documentation".
You are interested in Part One, Section 3, Tutorial: Euclid’s Presentation on page 21.