Gutters hang on the fascia board, and the fascia is usually the first thing to suffer when gutters overflow. Catching rot early means replacing a few boards instead of a whole side of the house.
Look for peeling or bubbling paint along the fascia, especially at the corners and near downspouts. Look for dark stains or green growth on the wood, and for gaps where the gutter has started to tip forward or pull away.
Sagging gutter runs are another sign. Hangers can only hold if the wood behind them is solid; when the screws lose their grip, the run drops and holds water, which speeds up the rot.
Finally, check the soffit underneath. Soft spots, holes, or signs of birds and squirrels getting in usually mean water has been working on the wood for a while.
The fix is to replace the damaged boards, prime and paint them, and correct whatever caused the overflow, whether that's clogs, poor pitch, or undersized downspouts.