As you face the field from your seats, lower number seats are on your right.
There is virtually no protection from the elements in the lower rows (or even the upper rows) in the 300 level at Gillette Stadium. Your seats will not be covered in the event of rain.
In Section 308 specifically, the one saving grace is that you are not in an exposed corner section where it is extra-windy and the rain can blow sideways. Additionally, Row 6 is close to the concourse tunnel, making it easy to run for shelter if needed.
As you look towards the field of play from your seats, lower numbered seats are on your right at Gillette Stadium.
Seating on the Patriots side of the field (Lower Level Sections 101-117) are on the east side of the stadium. Sections 109-117 in the lower level are the most west-facing sections in the stadium.