Let me explain what "скучать" means.

Generally, it expresses negative emotions related to sadness.

It has two usages.

1. "Скучать" as "to miss someone/something". In this case, it is used this way: [Subject in Nominative] + скучать (choose a proper form) по + [What or Who being missed in Dative].

It does not only mean "to miss", it expresses strong emotions of sadness or melancholy because of the missing thing/person.

Я скучаю по тебе. - I am missing you (now). That is why I am sad. I want to see you, but I cannot.
Я скучал по тебе. - in the past. That is what you say to your beloved one when you meet after a long separation.
Я буду скучать по тебе. - in the future. That is what you say to your beloved one when he/she leaves for a long time.

Я скучаю по дому. - I am missing my home. I feel homesick. I am sad because of that. I wish I would return home.
Я скучаю по Москве. - the same meaning: I am missing Moscow, and I am sad because of that.