Learn Russian: Вы постоянно противоречите мне.

The verb противоречить (to contradict) requires the dative case without a preposition. While in English you contradict a direct object, in Russian you direct your contradiction to someone. This fits the pattern of other verbs of interaction or assistance you are learning, like помогать (to help) or мешать (to bother).

Противоречите is a very long word. Is there a trick to remembering it?

Yes, breaking it down into its roots makes it much easier! It combines против (against) and a root related to речь (speech). So when you contradict someone, you are literally speaking against them.

Does the word постоянно mean we have to use the imperfective aspect?

Exactly. Постоянно (constantly) shows that this is a repeated, habitual action. Because the action is ongoing and not a single completed event, you must use the imperfective verb противоречить.

Could I change the word order and put мне earlier in the sentence?

You absolutely can. Russian word order is flexible, and Вы мне постоянно противоречите is a very natural, neutral alternative. Placing мне at the very end of the sentence, as shown here, puts a slight logical emphasis on it: you are contradicting me specifically, as opposed to someone else.