"The grandfather never says no."
Translation:Bedstefaren siger aldrig nej.
I believe your sentence is wrong, because Danish requires "verb second" (V2) word order for the main clause (similar to the rule that governs German and Dutch). You have the verb in the third spot; hence it's wrong.
In general, the adverb is immediately after the verb, but if the subject is inverted, the adverb comes after the subject; in other words, regardless of order, the subject and verb are a package deal. I believe both of these would be correct:
"Bedstefaren siger aldrig nej." "Nej siger bedstefaren aldrig."
(Someone please correct me if I'm wrong here!)
Trying to simplify for now. Indeed, the general order is Subject-Verb-Adverb (SVA). e.g. Bedstefaren siger aldrig nej
There are few exceptions. For now: 1) you have a question, so the verb is pulled to the front (VSA). In longer sentences that also happens often. e.g. Siger bedstefaren aldrig nej?
2) in the subordinate sentence (usually followed by a conjunction), the adverb is placed between the subject and the verb (SAV) e.g. Jeg er aldrig glad, fordi min bedstefaren aldrig siger nej
There are other rules, but for now I think this should help.