Learn Portuguese (Portugal): Vou fazer o plano na próxima semana.

To say you are 'going to' do something, you conjugate the verb ir (to go) and add the main verb in its basic dictionary form (the infinitive). Here, vou is the 'I' form of ir, and fazer means 'to make'. Together, vou fazer means 'I am going to make'. Notice you do not need a connecting word like 'to' between them in Portuguese.

Why isn't there a word for 'I' in front of vou?

In Portuguese, the verb ending usually tells you who is doing the action. Because vou is specifically the 'I' form of the verb ir, it already means 'I am going'. You do not need to add the pronoun eu (I) unless you want to add special emphasis.

Where does the word na come from in na próxima semana?

English just says 'next week', but Portuguese expresses this as 'in the next week'. The word na is a mandatory contraction of the preposition em (in) and the feminine word for 'the' (a). They merge together to make na.

Why is próxima placed before semana? I thought adjectives usually come after the noun.