Learn Portuguese (Portugal): O cão não pode entrar no supermercado.

Because it follows the modal verb poder. When you use poder (can/may) with another action, the second verb stays in its infinitive form. Here, pode is conjugated for the dog (he/it), and entrar stays as its base form.

Does não pode mean the dog is physically unable to enter, or just not allowed?

The verb poder can mean both "to be physically able to" (can) and "to have permission to" (may). In this context, it means the dog does not have permission to go inside.

Why do we use no before supermercado?

In Portuguese, the verb entrar is usually followed by the preposition em (in/into). Because supermercado is a masculine noun, em combines with the article o (the) to make no. So, entrar no literally means "to enter into the".

Why does não come before pode?

In Portuguese, negative words like não always go directly before the conjugated verb. You say não pode entrar (literally "not can enter"), instead of attaching it after the verb like we do in English with "cannot".