Sashh - Orthodox Jews can and do use the internet although the ultra-orthodox Hasidim are not likely to use it.
There are different levels of religious piousness within Judaism ranging from the ultra-orthodox Hasidim to secular Jewry. There are also different takes on customs depending whether you are Ashkenazi (descending from Europe), Sepharadi (descending from Spain, North Africa etc), Mizrahi (descending from Arabic countries etc) and various other Jewish ethnicities. Traditions also tend to differ a lot in terms of ceremonial customs amongst Jews from different ethnicities.
The ceremony itself is called the "Bris Milah" (Covenant of circumcision).
It is a good question that you ask but I think you will find there are a range of answers depending on whether you ask a Rabbi from an orthodox strand of Judaism or a Rabbi from a more liberal one. You will probably get different answers as a lot of Judaism is about analysis and interpretation and the orthodox Rabbi would probably say that the ceremony is integral whereas the liberal Rabbi would probably say that a circumcision is permitted without the ceremony but as I say, it would depend on various factors.
However, it is assumed that the Bris Milah and the actual circumcision should be done together as the ceremony is what validates the circumcision "in the eyes of God" but for example, Hasidic Jews would not consider secular Jews to be proper Jews anyway, so their version of the ceremony would probably not be acceptable to certain strands of Judaism anyway.