Hi,
thanks for your question.
Unfortunately, there's no "one-size-fits-all" solution here, as responsiveness for tables is very tricky, due to the way tables work in browsers. There's just no fixed behavior that tables can show here.
However, for certain tables, "fliping" might be an option. To use that in a TablePress table, please see this TablePress Extension: http://tablepress.org/extensions/responsive-tables/
Regards,
Tobias