first, index, pointer (AmE)
middle
ring, third, wedding
I noticed the ring on the third finger of her left hand.

little, pinky (AmE)
broken, dislocated, injured, severed
pointing
accusatory, accusing, warning
The teacher raised a warning finger and we stopped talking.

delicate, elegant, graceful, slender, slim
long
bony, lean, skeletal, skinny, thin
chubby, fat, plump, podgy (BrE), pudgy, stubby
calloused/callused, clawed, gnarled
gentle
She took off his bandages with gentle fingers.

capable, deft, nimble, skilful/skillful, skilled
Her nimble fingers undid the knot in seconds.

nervous, numb
shaking, shaky, trembling
clumsy
His clumsy fingers struggled with the buttons.

limp
cold, frozen, icy
extended, outstretched
intertwined
dirty, filthy, grubby, sticky
gloved
manicured
trigger

point
‘It was them!’ she cried, pointing an accusing finger at the boys.
The investigators pointed the finger of blame at the driver of the crashed bus. (figurative)

draw
The man drew a finger across his throat in a threatening gesture.

insert, jam, poke, put, shove, stick, thrust
Everyone put their fingers in their ears when the shooting started.

jab, stab
The protester was jabbing a finger aggressively at a policeman.

entwine, interlace, intertwine, lace, thread
He gently laced his fingers between mine.

hook
She hooked her fingers in the belt loop of his jeans.

hold up, raise
She raised a finger to her lips to ask for silence.

wag, waggle, wave, wiggle
‘None of that!’ cried the teacher, wagging her finger.

twiddle
Dad started twiddling his fingers nervously.

dip
I dipped my finger in the sauce and licked it.

lick
run, trace, trail
She ran her finger along the dusty shelf.
Sally trailed her fingers in the water idly.

drum, tap
He was drumming his fingers nervously on the arm of the chair.

click, snap
We were swaying and clicking our fingers in time to the music.
He snapped his fingers and the waiter came running.

shut, trap
The child needed treatment after trapping her finger in the car door.

cut, slice
break, dislocate
crook
He crooked a finger to tell us to go over to him.

clench, close, curl
Tina curled her slender fingers into a fist.

extend, spread, stretch, stretch out
He held up his hand with the fingers extended.

flex
prick
The nurse pricked my finger to get some blood.

bones, joints
movement
injury
puppet

with your fingers
It's easiest to eat corn with your fingers.

the finger of blame, the finger of fate, the finger of suspicion (all figurative)
The finger of suspicion was pointed at the construction company.

the tips of the fingers

Finger is used with these nouns as the object:
chin