Learn Turkish: Adamı bütün gün ormanda koşturuyorlar. - They are making the man run in the forest all day.

This is the core rule of causative case marking! The original verb is koşmak (to run), which is an intransitive verb (it doesn't take a direct object). When you make an intransitive verb causative, the person being made to do the action (the causee) becomes the direct object and takes the accusative case. So, "the man" becomes adamı.

How do we get the suffix -tur in koşturuyorlar?

The standard causative suffix is -dır. Here, it attaches to the verb root koş. Because ş is a hard (voiceless) consonant, the d changes to a t (consonant harmony). Then, because the vowel in koş is o, 4-way vowel harmony changes the suffix vowel to u. This gives us koştur-.

Could I say tüm gün instead of bütün gün here?

Yes, they mean exactly the same thing. Both bütün gün and tüm gün mean "all day" or "the whole day" and are completely interchangeable in everyday Turkish.

Why is ormanda placed immediately before the verb?

In Turkish, the information placed right before the verb carries the main focus or emphasis. By putting ormanda (in the forest) there, the speaker is slightly emphasizing the location where they are making him run, rather than the duration or the person.