Tired is the verb when your sentence reports that something tired someone, with that someone as the direct object: The long hike tired us. If you're describing a weary person, it's the adjective: I'm tired.
Was tired alone doesn't settle it. The form is genuinely ambiguous: it can be the adjective describing a weary state, as in I was tired after the trip, or a verb form pointing back to something that caused the weariness, as in The trip was what tired me in a sentence like The long hike tired us. The distinguishing question is what did the tiring, and the sections below take up how to tell which reading fits your sentence.
Everyday situations
Writing to a friend after a long day? Use the adjective: I'm tired. Your wording describes a weary state, no action involved.
Telling someone what caused the weariness? Try the verb with a direct object: The late meeting tired everyone. Something did the tiring, so the verb fits.
Composing an excuse about effort? I tired myself out rearranging the garage. The reflexive form shows the tiring action, not just a state.
When was tired doesn't settle it
Don't rely on was tired alone to decide. With be, both readings are grammatical: the adjective describing a weary state, or a passive-style verb form pointing back to something that did the tiring.
Ask what your sentence is about. If nothing in it names a cause, as in She was tired after lunch, the adjective reading is what you're communicating, and that's the natural choice.
If you name the cause, the verb reading becomes available: She was tired out by the noise or The noise tired her. Adding out or an explicit tiring subject signals the verb sense you want.
When you're unsure, reword around be: The climb tired her for the action, She's tired for the state. That sidesteps the ambiguity instead of arguing it.