Learn Russian: Открытка красивая.

In Russian, the verb "to be" is almost never used in the present tense. Instead of saying "The postcard is beautiful," you simply say the subject and the adjective right next to each other: Открытка красивая (literally "Postcard beautiful").

Why does the word красивая end in -ая?

Красивая (beautiful) is an adjective describing открытка (postcard). Because открытка ends in -а, it is a feminine noun. Russian adjectives must match the gender of the noun they describe, and -ая is the standard ending for feminine adjectives.

How do we know it translates to "The postcard" instead of "A postcard"?

Russian does not have articles like "the" or "a". You have to guess which one makes the most sense based on context. Because this sentence is stating a fact about a specific object, translating it as "The postcard" is the most natural fit in English.

Could I switch the word order and say "Красивая открытка" instead?

You can, but it changes the meaning slightly! Открытка красивая is a complete sentence meaning "The postcard is beautiful." If you put the adjective first (Красивая открытка), it usually just makes a phrase meaning "A beautiful postcard" rather than a full sentence.