Learn Russian: Им не нравятся твои шутки.

In Russian, expressing what someone likes works backwards compared to English. We literally say that something is pleasing TO someone. The person who likes it must be in the Dative case. Им is the Dative form of Они (they), so it means 'to them'.

Why do we use нравятся here instead of нравится?

The verb has to match the thing that is liked, because that thing is the actual grammatical subject of the sentence. Since шутки (jokes) is plural, we use the plural verb нравятся (are pleasing). If they didn't like just one joke (шутка), we would use the singular form нравится.

Where exactly does the negative word не go in sentences like this?

The negative word не goes directly before the verb it negates. So we put it right before нравятся. The literal translation of this sentence is: To them не (not) нравятся (are pleasing) your jokes.

Why is the word for 'your' spelled твои?

Possessive words like 'your' have to match the gender and number of the noun they describe. Because шутки (jokes) is a plural noun, you must use the plural form твои instead of the singular forms like твой (masculine) or твоя (feminine).