Combining an elemental and non-elemental skill book will produce a new skill book. It generally doesn't matter which skill book you use (Haste + Bull Horns gives the same result as Clear Mind + Tentacle Lash) unless one or both of the skill books is a source skill, in which case a higher level result occurs.

Combinations without source books:

Fire + Necromancy = Corpse Explosion (explode a corpse, deal damage)
Fire + Polymorph = Bleed Fire (enemies create fire surfaces when hit)
Fire + Warfare = Sparking Swings (melee attacks leap to second target)
Fire + Hunter = Explosive Trap (set up a trap, explodes when approached)
Fire + Scoundrel = Sabotage (grenade or arrow in targets inventory explodes)
Fire + Summoning = Fire Infusion (minion switches to fire and learns fireball)

Air + Necromancy = Vacuum Touch (damage, suffocation and silence)
Air + Polymorph = Vaporise (Turns surfaces into clouds and cures petrification and frozen)
Air + Warfare = Breathing Bubble (Immunity to clouds and suffocate)
Air + Hunter = Erratic Wisp (Target teleports randomly when hit)
Air + Scoundrel = Smoke Cover (Create a cloud centered on self)
Air + Summoning = Electric Infusion (minion switches to electric and learns eletric discharge)

Water + Necromancy = Blood Rain (douses fires, makes enemies bleed, blood everywhere)
Water + Polymorph = Healing Tears (generate tears that heal allies who move nearby)
Water + Warfare = Cleanse Wounds (heal, remove burn, disabled, decay, poison and bleed)
Water + Hunter = Cyrotherapy (convert nearby frozen ground into magic armour)
Water + Scoundrel = Vampiric Hunger (50% life steal for two turns)
Water + Summoning = Water Infusion (minion switches to water and gains restoration)

Earth + Necromancy = Corrosive Spray (Cone of damage, acid and atrophy)
Earth + Polymorph = Turn to Oil (Converts water/blood to oil and removes stuck and shock)
Earth + Warfare = Oily Carapace (Consume nearby oil to gain physical armour)
Earth + Hunter = Throw Dust (Damage, Blind, Removes surfaces and clouds)
Earth + Scoundrel = Venom Coating (Adds poison damage to weapon attacks, 2 turns)
Earth + Summoning = Poison Infusion (minion switches to poison and gains poison dart)

Combinations with source books:

Polymorph 2 + Fire 2 = Flaming Skin
Polymorph 2 + Water 2 = Icy Skin
Polymorph 2 + Air 2 = Jellyfish Skin
Polymorph 2 + Earth 2 = Poisonous Skin

Fire 2 + Necromancer 2 = Mass Corpse Explosion
Fire 2 + Warfare 2 = Master of Sparks
Fire 2 + Hunter 2 = Mass Exploding Traps
Fire 2 + Scoundrel 2 = Mass Sabotage

Summoning 2 + Earth 2 = Acid Infusion
Summoning 2 + Air 2 = Cursed Electric Infusion
Summoning 2 + Water 2 = Ice Infusion
Summoning 2 + Fire 2 = Necrofire Infusion
Summoning 2 + Necromancer 2 = Blood Infusion

(The second list is less detailed and probably incomplete, I'm playing through the game slowly with a partner so I'll be able to update this once we hit the point that we have a lot of source books to experiment with)

All skillbooks will be of the elemental element except for Blood Rain (which is necromancy) and all infusions (which are summoning).

All non-source skillbooks require level 1 in each of the two skills needed to make them, the source skillbooks require level 2 in each skill. Corrosive Spray is the exception, but it is likely a bug and the base Earth + Necromancy combo should be Corrosive Touch.

Information provided on what the skills do is a summary of the tooltip, rather than actual ability use. In many cases the tooltip is a little vague.

Most amusing combination award goes to erratic wisp which you should use on your allies constantly whether they like it or not.