badly, furiously, terribly, uncontrollably, violently
Her hands were shaking so badly that she couldn't hold her glass.

a little, slightly, etc.
almost, practically
He was almost shaking with the intensity of what he was saying.
Roxy was practically shaking with anger.

literally, physically
I was numb with dread. I was literally shaking.

visibly
nervously
My hands started shaking nervously.

from
My body was shaking from the cold.

with
She was shaking with anger/fury/rage.
to shake with fear/laughter/sobs

be shaking all over, be shaking from head to toe
He was crying and shaking all over.

be shaking in your boots (= be frightened), be shaking like a leaf
find yourself shaking
I found myself shaking uncontrollably with cold.

start shaking
I started shaking with fear.

stop shaking
I just couldn't stop shaking.

hard, roughly, vigorously, violently
He shook the blankets vigorously to get rid of the dust.
She must have shaken the baby very violently to inflict such severe injuries.

gently, lightly, slightly
well
Shake well before use.

suddenly

by
He shook her gently by the shoulders.

decisively, emphatically, firmly
fiercely, furiously, vehemently, vigorously, violently, wildly
a little, gently, lightly, slightly
quickly
slowly
dismissively, impatiently
despairingly, desperately, helplessly, miserably, mournfully, regretfully, ruefully, sadly, sorrowfully
wearily
disbelievingly, doubtfully
just, merely, only, simply
He merely shook his head.

silently
from side to side

at
He shook his head at her disbelievingly.

in
She shook her head in disbelief.

firmly, vigorously
warmly

shake sb by the hand
Our host shook each of us warmly by the hand.

Shake is used with these nouns as the subject:
arm, body, door, earth, earthquake, explosion, hand, knee, leg, shoulder, sob, thunder, tremor, voice

Shake is used with these nouns as the object:
belief, confidence, conviction, curl, dice, dirt, dust, faith, feeling, fist, foundation, ground, hand, head, hip, mane, world