How to easily use UTF-8 with LaTeX?

Editor's note:

This question addresses a specific case of UTF-8 character not working in LaTeX documents. Refer to Entering Unicode characters in LaTeX for other cases.

It's probably a stupid question, but I cannot find any easy answers online, and the answers are sometimes contradictory.

I am writing a document that uses a few strange alphabets. I want to use some LaTeX variant for typesetting, but nothing works. For example, if I take this document with four example words (one in Russian, one in Czech, one in latin with length indication, one in Vietnamese)

\documentclass[12pt,a4paper]{report}\usepackage[utf8]{inputenc}\begin{document}Днепр kůň dominī Ngữ\end{document}

and put it through xelatex, which people recommend for Unicode, all I get is this

which is not exactly what I want.

What is the easiest way of putting UTF-8 encoded file on one side and getting actual text on the other side?

edit:

To add more information.

I am using Ubuntu operating system, and I want to use some font appropriate for a bigger thesis (something like Computer Modern is fine, although I personally prefer Palatino-style fonts)