bs"d If you are a religious Jew and are put in a situation where you will be in a place for an extended period of time without a calendar and without knowing which day is Shabbat, can you just declare one day as Shabbat and then count seven days until the next Shabbat?

Shalom, I imagine from your question that you once heard of the famous g’mara in Shabbat 69, and cited by the Shulchan Aruch, (Or. Ch. 344, 1), but to be exact, the halacha is that you count 7 days from the day that you noticed that you don’t know the day of the week, and then hallow that 7th day as Shabbat. Nevertheless, in such a case, one couldn’t do prohibited work at all on the other days, unless necessary for his basic livelihood. Thank G-d, with modern calendars and cellphones, I think the question has become totally obsolete! With love of Israel, Rav Ari Shvat