Let us start with the simple rule: countries (more on that later, "countries" here not only means proper countries but also states or regions) are usually of neutral Genus and are named without any article at all:
Ich komme aus Sachsen.
Ich fahre nach Sachsen.
Ich lebe in Sachsen.
Sachsen ist schön.
People, however, are of the generic masculine Genus and have accordingly the article "der" in Singular, "die" in Plural:
Der Sachse (person) lebt in Sachsen (country).
Die Sachsen (people) sind in Sachsen (country) beheimatet.
As with any language, there is no rule without exceptions: I said that countries are usually of neutral Genus. In fact, there are some few countries, which are not of neutral Genus:
die Schweiz (fem.)
der Iran (masc.)
der Irak (masc.)
der Kongo (masc.)
der Sudan (masc.)
and
all countries ending on "-ei" are feminine, e.g. "die Lombardei", "die Türkei", etc.
So, here is the exception: all countries of masculine or feminine Genus retain their respective article:
Ich fahre nach Sachsen. but: Ich fahre in die Türkei.
It is possible to build the latter sentence similarily to the former:
Ich fahre nach der Türkei.
but this is outdated and sounds anachronistic today. You may find that in older texts, however.
Also notice that "Sachsen" (the people) can have a double meaning: there is the historic germanic tribe, the Saxons, which also settled in England (hence: "anglosaxon") and there are the people living in todays German state of Saxonia.