In German, there are bestimmte Artikel (definite articles) and unbestimmte Artikel (indefinite articles). For example
Er zieht den Schuh an.
refers to a specific shoe and therefore uses the definite article "der" (in the accusative form "den").
Er zieht einen Schuh an.
refers to about any shoe, not a specific one, and therefore uses the indefinite article "ein" (in the accusative form "einen").
The difference between "der" / "die" / "das" and "ein" / "eine" / "eines" is comparable to the difference between "the" and "a" in English:
He puts on the shoe.
He puts on a shoe.
But, all of those examples have been singular. What about the plural?
There is a definite article in plural, "die":
Er zieht die Schuhe an.
referring to specific shoes.
But there's no indefinite article in plural. In this case, the article is omitted:
Er zieht Schuhe an.
referring not to specific shoes, probably about any pair will do.
Again, it's quite similar in English,
He puts on the shoes.
He puts on shoes.
Additionally, there are other cases where you omit the article, for example where other languages would use a partive article (in French or Italian, for example):
Er kauft Brot.
refers to "bread" more as substance or as a material, not to a specific loaf of bread, or even to any loaf of bread. Again, compare to English
He buys bread.
In French, this would be
Il achète du pain. (« du » as a shortening of « de le »)
In this case, the article gets omitted in singular and plural. Here, the difference between singular and plural refers to whether the object in question is countable:
Er kauft Wasser. ("Wasser" can't be counted, there's no "ein Wasser", "zwei Wasser" and so forth, you'd need a unit like "one glass of water".)
Er kauft Kekse. ("Kekse" can be counted, "ein Keks", "zwei Kekse" and so forth.)
There are some nouns that can be used as either countable or uncountable. For example,
Er kauft Brot.
Er kauft Brote.
would both be correct, but with slightly different meanings.
And as an aside, "eine Schuhe" doesn't exist. In this case, "Schuhe" would be a singular feminine noun. But "Schuhe" is the plural of "Schuh". Therefore, it would need to be either "ein Schuh" or (as explained above) "Schuhe" with the article omitted.