der Föhn
hair dryer
An electrical device that produces a stream of warm air to dry hair.
Ich muss mir noch schnell mit dem Föhn die Haare trocknen, bevor wir gehen.
I quickly need to dry my hair with the hair dryer before we go.

hair dryer / foehn
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hair dryer
An electrical device that produces a stream of warm air to dry hair.
Ich muss mir noch schnell mit dem Föhn die Haare trocknen, bevor wir gehen.
I quickly need to dry my hair with the hair dryer before we go.

The context tells you whether the device or the wind is meant. If you are talking about hair, the bathroom, or electrical appliances, it means the hair dryer. If it is about weather, the Alps, wind, or headaches, it means the weather phenomenon.
Kannst du mir den Föhn geben? Meine Haare sind noch nass.
Can you give me the hair dryer? My hair is still wet.
The verb 'föhnen' (to blow-dry) is derived from the noun 'der Föhn' (hair dryer). So you can say: 'Ich trockne meine Haare mit dem Föhn' (I dry my hair with the hair dryer) or, more briefly: 'Ich föhne meine Haare' (I blow-dry my hair).
Nach dem Schwimmen föhne ich mir immer die Haare.
After swimming, I always blow-dry my hair.
The foehn wind as a weather phenomenon is often associated with physical discomfort. Typical statements are that you 'bei Föhn Kopfschmerzen hat' (have headaches when there is a foehn wind) or 'sich wegen des Föhns unwohl fühlt' (feel unwell because of the foehn wind).
Meine Großmutter spürt den Föhn immer in ihren Gelenken.
My grandmother always feels the foehn wind in her joints.
dryer
'der Trockner' and 'der Föhn' can both be devices that dry something with warm air. In everyday language, however, 'Trockner' usually means a large appliance for laundry. More generally, a 'Trockner' can also be a device that dries something else. 'Föhn', by contrast, means a small device for drying hair. The words can be confused because both have to do with air and drying. For clothes, you normally say 'Trockner'; for hair, 'Föhn'.

Vor der Arbeit trocknet Anna ihre Haare schnell mit dem Föhn.
Before work, Anna quickly dries her hair with the hair dryer.
Nach dem Waschen kommt die Bettwäsche direkt in den Trockner.
After washing, the bed linen goes straight into the dryer.