absteigen
to dismount
To get down or climb down from something, especially from a bicycle, a horse, or a mountain.
Er musste vom Fahrrad absteigen, weil der Hügel zu steil war.
He had to dismount from his bicycle because the hill was too steep.

to dismount / descend
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to dismount
To get down or climb down from something, especially from a bicycle, a horse, or a mountain.
Er musste vom Fahrrad absteigen, weil der Hügel zu steil war.
He had to dismount from his bicycle because the hill was too steep.

'Absteigen' (to dismount/descend) is a separable verb. In a main clause, the prefix 'ab-' comes at the end of the sentence. In subordinate clauses or in the infinitive with 'zu', the verb is not separated.
Der Radfahrer stieg vor dem steilen Berg ab.
The cyclist dismounted before the steep hill.
Because 'absteigen' (to dismount/descend) describes movement or a change of state, the perfect tense is always formed with the auxiliary verb 'sein' (to be).
Sie ist vom Pferd abgestiegen.
She dismounted from the horse.
The preposition helps you recognize the meaning: 'von etwas absteigen' (to dismount from something: bicycle, horse), 'in eine Liga absteigen' (to be relegated to a league: sports), or 'in einem Hotel absteigen' (to stay in a hotel: lodging).
Er stieg vom Rad ab, um eine Pause zu machen.
He got off his bike to take a break.
This meaning is used almost exclusively in sports. It describes a team moving to a lower division at the end of a season.
Wenn das Team das nächste Spiel verliert, steigt es ab.
If the team loses the next game, it will be relegated.
In the meaning 'Unterkunft nehmen' (to take lodging), 'absteigen' (to stay) is rather formal or literary. It sounds somewhat more elevated than everyday verbs.
Der Gesandte stieg im vornehmsten Hotel der Stadt ab.
The envoy stayed at the most distinguished hotel in the city.
to fall
'fallen' and 'absteigen' can both have to do with downward movement. The important difference is control. 'fallen' usually happens unintentionally and often suddenly: a person falls, or an object comes down. 'absteigen' is usually a deliberate movement downward, for example getting off a bicycle or horse, or descending a mountain. Learners may confuse the words because both have a downward direction. If someone controls the movement themselves, 'absteigen' usually fits. If something comes down uncontrollably, 'fallen' fits.

Vor der roten Ampel steigt Lisa vom Fahrrad ab.
Lisa gets off her bicycle before the red light.
Auf der nassen Treppe ist Samir fast gefallen.
Samir almost fell on the wet stairs.