Italian is the one adjective English uses for anything tied to that country. It covers where a thing is from (Italian olive oil), who a person is (my Italian neighbour), and which language is being used (an Italian newspaper). English always writes it with a capital I, even in the middle of a sentence, because the names of countries, peoples and languages keep their capital letter wherever they stand. One habit worth noticing: English puts the adjective straight in front of the noun with nothing between them — Italian coffee, where Chinese would put a 的 in the middle.

This is the adjective standing on its own, with the word person left out: an Italian is an Italian person. Because it names a person, it takes a/an and it has a plural, Italians. It keeps its capital letter. English allows this shortcut with some nationality words and not others, so it is worth checking each country name rather than assuming — but with this one it is completely ordinary. To talk about the people as a whole you will see both Italians and the Italians.

As a language name, Italian is uncountable: you learn Italian, you speak Italian, you say something in Italian — never an Italian and never Italians. That is the quick way to tell this sense from the person sense. An a, an or -s in front of you means a person; a bare Italian after speak, learn, study, teach or in means the language. Note the preposition: say it in Italian, a menu in Italian. After speak there is no in — she speaks Italian — although speak in Italian does appear when the point is which language someone switched into.