Otec přivázal pes k bouda.

The main verb is "přivázal" 3sg. past tense form of přivázat "to tie someone/something onto"

The subject is the nominative form otec.

The verb přivázat takes a direct object in the accusative; bouda is not a good candidate for the accusative since it is preceded by the preposition "k"; also it wouldn't make sense to think that the father tied the kennel onto something. Thus, pes should be the direct object.

přivázat also takes a prepositional phrase k + dative case; bouda should be in the dative case.