Brúin er opin.

Icelandic doesn’t have a separate definite article like English the. Instead you attach a suffix to the noun. Here brú (“bridge”) is a feminine noun, and the definite singular ending for many feminine nouns is -in:
• brú → brúin (“the bridge”)

You usually check a dictionary, which will list the gender. As a rule of thumb, many Icelandic nouns ending in -u in the nominative singular are feminine. Also, the form of the definite suffix gives a clue:
• Feminine sg def: -in (one “n”)
• Masculine sg def: -inn (two “n”s)

Since brúin has only one “n,” it’s the feminine form.

Adjectives in Icelandic agree with the noun’s gender, number and case. This sentence uses opin because:

1. “open” is traditionally opinn in the masculine nominative singular.
2. The feminine nominative singular form is opin.
3. In Brúin er opin, both noun and adjective are nominative singular feminine.

In the strong (basic) declension you get:
• Masculine nominative sg: opinn
• Feminine nominative sg: opin
• Neuter nominative sg: opið
• Plural nominative (all genders): opnir

Icelandic adjectives have two main declension patterns:
• Strong (basic) endings when used predicatively (after vera, virka, etc.), or attributively with an indefinite noun.
• Weak endings when used attributively with a definite noun (one that already carries the article-suffix).

Examples:
• Predicative: Brúin er opin. (strong feminine opin)
• Attributive definite: opna brúin (“the open bridge”; weak feminine opna)

1. “Bridge” in nominative plural indefinite is brýr.
   
   2. Definite plural ending for feminine 1st-declension nouns is -nar: brýrnar.
   3. “are” (3 pl.) = eru.
   4. Adjective “open” in nominative plural = opnar.

Put together:
 Brýrnar eru opnar.
(“The bridges are open.”)

No—brú without -in is indefinite (“a bridge”), so brú er opin means “a bridge is open.” To say “the bridge is open,” you must use the definite form brúin.

Phonetic approximation in IPA:
 /brˠuːɪn ɛr ˈɔːpɪn/

Breakdown:
• ú = [uː] (long “oo”)
• i in brúin = [ɪ] (as in English “bit”)
• e in er = [ɛ] (as in English “bet”)
• o in opin = [ɔː] (as in English “law”)

1. Dictionary gives hurð (feminine).
2. Add feminine sg def -in → hurðin (“the door”).
3. Use predicative adjective opin (fem. nom. sg).

Result:
 Hurðin er opin. ("The door is open.")