If the player knows any of these vanilla spells, they can teach them to Serana. Expanded vanilla spell support and mod support is eventually planned.
Conjure Bound Dagger
Conjure Bound Sword
Conjure Familiar
Conjure Bound Battleaxe
Summon Flaming Familiar
Courage
Lesser Ward
Steadfast Ward
Turn Lesser Undead
Frost Cloak
Lightning Cloak
Whirlwind Cloak
Wall of Frost
Wall of Storms
Paralyze
Mass Paralysis
Dragonhide
Conjure Dremora Lord
Fury
Calm
Frenzy
Rally
Pacify
Rout
Lightning Rune
Icy Spear
Thunderbolt
SDA also supports Apocalypse via a plug-and-play integration (no patch needed). Here are the spells from that mod that you can teach Serana.
Apocalypse
Battletide
Blood Boil
Blood for Blood
Bloodseeker
Bolide
Bone Spirit
Circle of the Moons
Conjure Dremora Churl
Conjure Dremora Pit Fighter
Conjure Dremora Champion
Conjure Dremora Honor Guard
Conjure Xivlai Sorcerer
Conjure Xivlai Lord
Crackle
Curse of the Silent
Electrosphere
Empathic Agony
Evil Twin
Forbidden Sun
Frozen Orb
Godform
Hailstone
Howling Blasz
Ice Shiv
Illusory Flames
Illusory Pyre
Lamb of Mara
Leech Seed
Lightning Strike
Magicka Void
Malviser’s Gauntlet
Resurgence
Seidstone
Shroudwalk
Sotha’s Maelstrom
Soul Cloak
Tharn’s Prison
Tumble Magnet
Wyrd
Additionally, Serana starts off with additional (leveled) spells that become more powerful as she levels up.
STAGE 1 SPELLS
Oakflesh
Conjure Flame Atronach
Healing
STAGE 2 SPELLS
Stoneflesh
Conjure Ice Atronach
Fast Healing
STAGE 3 SPELLS
Ironflesh
Conjure Storm Atronach
Close Wounds
STAGE 4 SPELLS
Ebonyflesh
Conjure Wrathman
Grand Healing
Note: (Except for Flaming Familiar and Conjure Flame Atronach) Serana cannot learn fire spells. She's a vampire, and even if cured she would still have a fear of fire. Flaming Familiar is the exception because it technically is a magic homing missile, summoned from a distance. Same with the Flame Atronach.