Learn Russian: При подключении к интернету просто нажимаешь эту кнопку. - When connecting to the internet, you just press this button.

Both are correct, but при + Prepositional case allows you to express a condition or circumstance using a noun rather than a full verb clause. Here, при подключении literally means "at the time of connection" or "upon connection". It sounds a bit more concise and is very common in instructions or manuals.

Why does интернет take the preposition к and the Dative case (к интернету) right after a noun?

Because подключение is a verbal noun (a noun derived from a verb). The verb it comes from, подключаться (to connect), requires к + Dative to indicate what you are connecting to. Verbal nouns usually keep the exact same case and preposition requirements as their parent verbs.

Why does подключении end in -ии in the Prepositional case?

Neuter nouns that end in -ие in the Nominative case (like подключение, здание, упражнение) are an exception to the standard Prepositional -е ending. They take -ии in the Prepositional case.

There is no pronoun ты (you) in the sentence, so why is the verb нажимаешь conjugated in the second person?