how to watch last week's X-Files?

Hulu is your best mainstream option.

But I would recommend buying a AmazonTV and downloading Kodi.

If you have Cox, OnDemand is the way to go.
It probably helps to watch last week's episode, because two characters get introduced that pop up in the finale. Although last week's episode wasn't that great and the finale was even worse, so you may be better off reading a book, baking a loaf of bread, taking a bubble bath or jacking off.