The key tip is to prevent the straw from drying out over time. You can lightly steam it occasionally, using a steamer or steam from a kettle, or by taking it into the bathroom while showering. Alternately you can lightly mist it with a spray bottle.
It is a mistake to pick up the hat by the pinch or the crown. Your fingertips will weaken the fibres over time and they will start to split and fray. Always pick your hat up by the inside of the crown. Set it down upsaidedown, resting on the crown to avoid bending the brim.
If the hat gets something on it: Spot clean using a damp cloth with mild soapy water or a wet wipe using gentle strokes following the grain of the fibres. Be sure not to rub the stain further into the weave. Pat dry and allow the hat to dry naturally. Do not use chemical cleaners as this may stain and cause discolouration.
Reshaping: over time, a Panama hat may need to be refreshed or reshaped. Dampen both inside & outside of the hat using the steam of an iron, holding it about 5 cm from the iron. Gently stuff the crown with plain white tissue paper to the desired shape. Leave in a well-ventilated place to dry with the crown and brim supported. If you need to straighten the brim of your hat, you can iron it on a very low heat with a cloth between the iron and the hat to prevent the delicate fibers of the hat from burning.