We are lead to believe from the text that either Draco already knew how to cast this spell, or that this spell was simple enough that a second year student could perform it fairly easily.
Snape moved closer to Malfoy, bent down, and whispered some-
thing in his ear. Malfoy smirked, too.
But Lockhart wasn’t listening.
“Three — two — one — go!” he shouted.
Malfoy raised his wand quickly and bellowed, “Serpensortia!”
The end of his wand exploded. Harry watched, aghast, as a long
black snake shot out of it, fell heavily onto the floor between them,
and raised itself, ready to strike.
“Don’t move, Potter,” said Snape lazily, clearly enjoying the sight
of Harry standing motionless, eye to eye with the angry snake. “I’ll
get rid of it. . . .”
As we can see Draco didn't appear to have to learn any wand movements, and just had to yell the curse for the snake to appear.
We do know conjuring spells are not all, very advanced, the spell to summon water for one, as well as the Spell Hermione uses to summon her blue fire, which she had perfected in her first year.
From earlier in the same year we see ron is able to summon/conjure up slugs.
A loud bang echoed around the stadium and a jet of green light
shot out of the wrong end of Ron’s wand, hitting him in the stom-
ach and sending him reeling backward onto the grass.
Ron opened his mouth to speak, but no words came out. Instead
he gave an almighty belch and several slugs dribbled out of his
mouth onto his lap.
“I don’t think there’s anything to do except wait for it to stop,”
said Hermione anxiously, watching Ron bend over the basin.
“That’s a difficult curse to work at the best of times, but with a
bro- ken wand —”