Learn Finnish: Korjautan vanhan auton huomenna. - I will have the old car repaired tomorrow.

The verb comes from korjauttaa, which is a curative verb. It is formed by taking the basic verb korjata (to repair) and adding the suffix -uttaa. This suffix indicates that you are commissioning or having someone else perform the action.

How exactly is the suffix -uttaa attached to korjata to get korjauttaa?

For Type 4 verbs like korjata, you first find the vowel stem by dropping the infinitive ending, which gives korjaa-. Then, you shorten the long vowel at the end of the stem to a short vowel (korja-) before adding the -uttaa suffix.

Why is the object vanhan auton in the genitive-looking accusative case instead of the partitive?

Even though the verb is curative, normal object rules apply. The action of having the car repaired is seen as a complete, bounded action that will be finished. Because it is an affirmative sentence with a complete action, the total object takes the genitive-accusative ending -n.

How does the grammar show that this is happening in the future, given there is no future tense verb?

Finnish does not have a separate future tense. Instead, it uses the present tense verb korjautan combined with the time word huomenna (tomorrow). The use of the total object vanhan auton also heavily reinforces that this is a complete action that will be finished in the future.