This is the 7788th most frequent Russian word.
интернетом
"Интернетом" means "by/with the Internet" (instrumental case of "интернет").
The instrumental case 'интернетом' is used here to indicate the means by which the action is performed (using the internet).
Я пользуюсь интернетом каждый день.
I use the internet every day.
The instrumental case 'интернетом' here shows the medium through which information is shared.
Мы делились новостями через интернетом.
We shared news through the internet.
The instrumental case 'интернетом' is used to describe the object of interest after the verb 'увлекаться' (to be interested in a subject).