müde
tired
Feeling the need for sleep or rest; being physically or mentally exhausted.
Nach der langen Wanderung war ich sehr müde und bin sofort eingeschlafen.
After the long hike, I was very tired and fell asleep immediately.

tired
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tired
Feeling the need for sleep or rest; being physically or mentally exhausted.
Nach der langen Wanderung war ich sehr müde und bin sofort eingeschlafen.
After the long hike, I was very tired and fell asleep immediately.

The adjective 'müde' (tired) is most often combined with the verbs 'sein' (to be), 'werden' (to become/get), or 'aussehen' (to look). It describes either a state or a change.
Ich bin heute wirklich müde.
I am really tired today.
When 'müde' (tired) refers to a person, it usually means 'schläfrig' (sleepy). When it refers to a material such as metal or plastic, the technical meaning 'an Festigkeit verloren' (having lost strength) is meant. The construction 'etwas müde sein' means 'einer Sache überdrüssig sein' (to be tired of something).
Der Läufer war nach dem Marathon völlig müde.
The runner was completely tired after the marathon.
To express that you have had enough of something, you use the construction 'etwas (Akkusativ) müde sein' or 'es müde sein, etwas zu tun'. The person who is fed up with something is the subject of the sentence.
Ich bin diesen langen Winter müde.
I am tired of this long winter.
The meaning 'an Festigkeit verlieren' (to lose strength) is technical language from materials science and engineering. In everyday life, 'müde' (tired) is almost never used in this context.
Nach Millionen von Biegungen wurde die Feder müde und brach.
After millions of bends, the spring became fatigued and broke.
fresh
'frisch' and 'müde' are opposites when talking about a person's energy and condition. In this sense, 'frisch' means that someone is rested, alert, and full of energy. 'müde' means that someone needs sleep or rest and has little energy. After a good night, you are more likely to feel frisch. After a long workday or a long trip, you are more likely to be müde. This contrast is not about food or weather, but about a physical or mental state.

Am Wochenende ist meine Freundin nach der langen Fahrt sehr müde.
At the weekend, my friend is very tired after the long drive.
Am Morgen nach dem Urlaub fühlt sie sich wieder frisch.
On the morning after her vacation, she feels fresh again.