How do I write plural messages in ICU message format? 

Use a plural argument. Its branches are named after the CLDR plural categories of the message's language, # is replaced by the number formatted for that locale, and the other branch is mandatory.

{count, plural, =0 {No items} one {# item} other {# items}}

In English this prints No items, 1 item and 1,000 items for 0, 1 and 1000.

Selection happens in two steps. The value is first compared with the exact matches (=0, =1 and so on). If none applies, the locale's plural rules map it to one of the categories zero, one, two, few, many and other, and a category without a branch falls back to other. Which categories a language uses differs: English has one and other, Russian has one, few, many and other, Arabic uses all six and Japanese only other. The per-language lists are in the CLDR plural rules chart and on the language plural rules page.

offset:n subtracts n before the category is chosen and before # is printed, while the exact matches still see the original value:

{count, plural, offset:1
  =0 {Nobody liked this}
  =1 {You liked this}
  one {You and # other person liked this}
  other {You and # others liked this}}

For 3 this prints You and 2 others liked this.

Java's java.text.MessageFormat has no plural type. Its ChoiceFormat picks a branch by numeric range and, as its javadoc states, "doesn't implement any locale specific behavior", so it cannot produce the Russian or Arabic forms. Use ICU4J's com.ibm.icu.text.MessageFormat (Maven artifact com.ibm.icu:icu4j), which takes named arguments in a map:

import com.ibm.icu.text.MessageFormat;
import java.util.Locale;
import java.util.Map;

String pattern = "{count, plural, one {# файл} few {# файла} many {# файлов} other {# файла}}";
MessageFormat format = new MessageFormat(pattern, Locale.forLanguageTag("ru"));
String text = format.format(Map.of("count", 21)); // "21 файл"

Translators must write the categories of their own language instead of copying the source branches. An English one/other message translated into Polish needs one, few, many and other; with few missing, 2 would print the other form. The ICU message format for translators page explains this from the translator's side, and the ICU message editor shows which branch a value selects in a given language.