spülen
to wash
To clean dishes, cutlery, and pots with water and dish soap.
Nach dem Abendessen muss ich noch das Geschirr spülen.
After dinner, I still have to wash the dishes.

to wash / rinse / flush
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to wash
To clean dishes, cutlery, and pots with water and dish soap.
Nach dem Abendessen muss ich noch das Geschirr spülen.
After dinner, I still have to wash the dishes.

The verb 'spülen' (to wash/rinse/flush) is the stem for several useful nouns. 'Die Spüle' (sink) is the place where you wash dishes, 'die Spülmaschine' (dishwasher) is the appliance for it, and 'die Spülung' (flush/rinse) is the process, e.g. for the toilet or for hair.
Stell das schmutzige Geschirr bitte in die Spüle.
Please put the dirty dishes in the sink.
The exact meaning of 'spülen' (to wash/rinse/flush) depends strongly on the object. 'Geschirr spülen' means to wash dishes, 'den Mund spülen' means to rinse your mouth, and in the bathroom 'spülen' usually refers to flushing the toilet.
Nach dem Zähneputzen sollst du den Mund gut spülen.
After brushing your teeth, you should rinse your mouth well.
When it is about dishes, 'spülen' (to wash) is often combined with 'von Hand' (by hand) or, in contrast, 'mit der Spülmaschine' (with the dishwasher). You can also simply say 'spülen' if the context is clear.
Ich spüle lieber von Hand, als die Spülmaschine zu benutzen.
I prefer washing dishes by hand to using the dishwasher.
In this meaning, the water (e.g. the sea, the river) is the subject of the sentence. What is moved is the accusative object, and the direction is often indicated with 'an' + accusative.
Die Flut hat viel Treibholz an die Küste gespült.
The tide washed a lot of driftwood onto the coast.
to wash
'waschen' and 'spülen' can both mean that something is cleaned with water. 'waschen' is broader and fits especially with clothes, hands, or also things that you clean with water and soap. 'spülen' is very often used for dishes, cutlery, and pots. It can also mean to rinse something through or wash something off with water, for example your mouth or a bottle. Learners may confuse the words because you can sometimes hear both for dishes. But 'spülen' is more precise there, while 'waschen' is more general.

Wenn alle gegessen haben, spült Tom die Teller und die Töpfe.
When everyone has eaten, Tom washes the plates and pots.
Nach dem Kochen wasche ich mir die Hände mit Seife.
After cooking, I wash my hands with soap.