Finnish has no indefinite or definite article like the English “a” and “the”. This may sound uncomfortable if you are accustomed to the article system of English. However, Finnish, like many other languages, works well without articles.
For example, in English we might start a story by telling “Yesterday I saw a fox” and later refer to “the fox”. The articles “a” and “the” are part of English grammar, but they don’t really have much of a role here. The situation is usually just as clear, from the context, when we say in Finnish Eilen näin ketun and later use just the word kettu without an article.
In spoken Finnish, the numeral yksi (colloquial form: yks) is often used much like an indefinite article, and the demonstrative pronouns se and tämä (colloquial form: tää) and sometimes tuo (colloquial toi) are used like a definite article. Thus, people might say Eilen mä näin yhden ketun and later refer to the fox as se kettu or, less often, tää kettu or occasionally toi kettu. Scholars disagree on the interpretation of the situation. Some say that spoken Finnish already has articles, others say that there are just signs of increasing article-like use of words and perhaps a competition between tämä and se on becoming the definitive article.
Standard Finnish rules do not allow article-like usage of demonstrative pronouns, but expressions like tämä kettu can be used when there is a specific reason to use a demonstrative pronoun for clarification. On the other hand, tämä is often used when there is no such reason. When something has just been mentioned (e.g, Tuolla on kettu “There is a fox over there”), a noun (like kettu) can be used as such, since the context establishes a definitive meaning for it. A typical reason for using tämä as an attribute is that you are physically pointing at something.
The use of eräs or yksi (yks) is often necessary in a manner that makes them indefinite articles in a limited sense. The English expression A man gave me this phone cannot really be translated without using eräs or yksi or some equivalent expression (such as muuan). So we write Eräs mies antoi minulle tämän puhelimen and perhaps say Yks mies anto mulle tän puhelimen. If we started the sentence with mies, it would effectively be definite, just like the English expression “the man”.
In formal writing, people often use the adjective kyseinen (or the longer expression kyseessä oleva) or asianomainen or the abbreviation ko. or ao., all meaning “the one in question”, for indicating something as definite. This is not regarded as incorrect, but it is clumsy style.