Learn French: J'aime caresser mon chien tous les jours.

You would say Caresse-le ! To give an affirmative command, you use the imperative form of the verb (caresse) and attach the direct object pronoun (le) to the end with a hyphen. Note that for -er verbs like caresser, the informal tu command drops the final "s".

Why is caresser in the infinitive form here?

When two verbs appear right next to each other, like J'aime and caresser, the first verb is conjugated to match the subject and the second verb stays in the infinitive (the dictionary form). This perfectly matches the English "I like to pet".

Is caresser the normal word for petting a dog? It sounds like "to caress"!

Yes, it is the standard, everyday verb for "to pet" an animal in French. While it looks like the English word "caress", it doesn't carry the same romantic or formal undertones when you are talking about pets.

Why use tous les jours instead of chaque jour for "every day"?

Both are correct and mean the same thing, but tous les jours (literally "all the days") is the most natural and common way to say "every day" in spoken French. Make sure to use the plural tous to match the masculine plural jours.