drücken
to press
To apply pressure deliberately to something with your fingers or hand, for example to a button or switch.
Du musst den roten Knopf drücken, um die Maschine zu starten.
You have to press the red button to start the machine.

to press / hug
Loading your saved state.
to press
To apply pressure deliberately to something with your fingers or hand, for example to a button or switch.
Du musst den roten Knopf drücken, um die Maschine zu starten.
You have to press the red button to start the machine.

The expression 'sich vor etwas drücken' (to shirk something) is reflexive and always uses the preposition 'vor' with the dative. It means to avoid an unpleasant task.
Er drückt sich immer vor der Hausarbeit.
He always shirks the housework.
The idiom is 'jemandem die Daumen drücken' (to keep one's fingers crossed for someone). The person you are wishing luck to is in the dative.
Ich drücke dir die Daumen für deine Prüfung morgen!
I'll keep my fingers crossed for your exam tomorrow!
In the meaning of 'pressen' (to press), the verb is often used with objects such as 'einen Knopf' (a button), 'eine Taste' (a key/button), 'einen Schalter' (a switch), or 'eine Türklinke' (a door handle).
Um den Computer zu starten, musst du den Power-Knopf drücken.
To start the computer, you have to press the power button.
This meaning can be literal, for example when clothing is too tight. But it can also be used figuratively for worries or problems that weigh on a person.
Diese Jacke drückt mich an den Schultern.
This jacket is pressing on my shoulders.
When 'drücken' (to hug) means 'umarmen' (to embrace), it is often described more precisely with adverbs such as 'fest' (tightly), 'herzlich' (warmly), or 'lange' (for a long time).
Zur Begrüßung drückte er seinen alten Freund herzlich.
In greeting, he hugged his old friend warmly.
In the meaning of 'senken' (to lower), 'drücken' (to push down) is used almost exclusively in a business context. Typical objects are 'Preise' (prices), 'Kosten' (costs), 'Löhne' (wages), or 'Margen' (margins).
Die Konkurrenz versucht, die Preise zu drücken.
The competition is trying to push prices down.
to pull / move
'ziehen' and 'drücken' both describe a movement involving force, but in opposite directions. With 'ziehen', you move something toward yourself or along behind you. With 'drücken', you apply pressure to something, often with your hand or fingers, for example to a button. The words are especially easy to confuse with doors, switches, or devices. A practical rule: if something is supposed to come toward you, it is 'ziehen'; if you exert force against something, it is 'drücken'.

Nach dem Essen drückt Paul auf den Knopf der Kaffeemaschine.
After eating, Paul presses the button on the coffee machine.
Bitte ziehen Sie die Tür langsam auf.
Please pull the door open slowly.