Learn Icelandic: Við sjáum flugvélina í dag.

Strong verbs generally only change their stem vowel for singular subjects (I, you, he/she/it). Because við (we) is plural, the verb keeps the original á from the infinitive sjá, adding the standard -um ending for "we". If the sentence were "I see", you would see the vowel change: ég sé.

Why does flugvélina end in -ina?

That ending is the attached definite article, meaning "the". Flugvél (airplane) is a feminine noun. Because it is the direct object of the verb (the thing being seen), it must be in the accusative case. For feminine nouns in the accusative, the attached "the" is -ina.

Is flugvél made up of two different words?

Yes! Icelandic frequently builds modern vocabulary by combining older words. Flug means "flight" and vél means "machine" or "engine". So, an airplane is literally a "flight-machine".

Doesn't í dag literally mean "in day"?

Exactly. To say "today", Icelandic uses the preposition í (in) followed by dag (the accusative form of dagur, meaning "day"). It is a fixed phrase you will use very often, so it is best to memorize it as a single chunk.