Learn Icelandic: Þau hafa planað ferðalagið.

Planað is the supine (the form used with the verb 'to have') of the verb plana (to plan). Plana is a Group 1 weak verb, which means it takes an -ar ending in the present tense (hún planar). To make the supine for this group, you just take the infinitive (plana) and change the final -a to -að.

How does the present perfect tense work in this sentence?

Just like in English, Icelandic uses the verb hafa (to have) plus the supine form of the main verb to talk about completed actions or past experiences. Here, we use hafa because the subject þau is plural, and we pair it with the supine planað to mean 'have planned'.

Why does the sentence use þau for 'they'?

Þau is the neuter plural pronoun for 'they'. In Icelandic, if a group consists of both males and females, or if the genders are mixed or unknown, you always use the neuter form þau. If the group were entirely male, it would be þeir, and if entirely female, þær.

What case is ferðalagið in?

It is in the accusative case because it is the direct object receiving the action (it is the thing being planned). The base word is the neuter noun ferðalag (trip or journey), and the -ið at the end is the attached word for 'the', making it 'the trip'. Luckily, for neuter words like this, the accusative form looks exactly the same as the dictionary form.