How do you remember which spells to use?

I'll try to simplify the "Rules" on what a spell will do depending on the elements contained. It's a fairly complex tree, which is what makes Magicka so fun - the diverse ways of blowing everything up.

Spells Containing Shield [E]

Self-Cast (middle mouse)

1) Containing Rock [D] or Ice [QR] - Personal Armor, Rock elements increase strength and decrease movespeed. Ice elements do the same to a lesser degree but cause contact damage and knockback when moving into enemies quickly.

2) Any other elements - Magic Immunity Aura that protects against elemental damage and status effects from any included elements. Multiples of a single element increase range and duration.

3) No extra elements (Just E) - Personal Shield that reflects beam spells away and blocks incoming damage. Any physical damage taken will cause a knockdown, and the shield drains quickly, although it can be boosted with healing elements or by pressing [spacebar]

Normal cast (right mouse), AoE cast (Shift+right mouse), Weapon Imbue (Shift+left mouse)

All three cast types create the same effect in a different pattern. Normal cast covers a semicircle in front of you, AoE cast covers an entire circle around you, and Weapon imbues cover a line in front of you.

1) Containing Rock [D] or Ice [QR] - Rock walls have a high amount of health and make strong barriers that slowly degenerate. They spew out sprayed elements (Fire, Water, Steam) and release beam elements (Arcane, Life) when destroyed. Ice walls have very low health and degenerate in mere seconds. They constantly damage the area around them with any additional elements, and release an explosion of those elements around them when they are destroyed.

2) Containing Arcane [S] or Life [W] - Mines that explode with arcane energy when stepped on. Arcane mines include high knockback.

3) Containing Sprayed Elements [Q or F or QF] - Storms hover in place for a while, indestructible, while expending their energy on whatever walks into them.

4) No extra elements (Just E) - Area Shield that follows the same properties of Personal Shield above.

Spells NOT Containing Shield [E]

Spells Containing Rock [D]

Spells of this type launch a projectile which does physical damage on contact and explodes upon hitting the ground, releasing any additional elements as AoE damage around the impact. The exception to this is Ice [QR], which causes the projectile to be single target but adds more damage than adding Rock elements. Rock elements increase the size and momentum.

1) Self-cast - Causes a rock to fall upon the caster's head. Typically the best way to commit suicide is to charge 5 Rocks and self cast.

2) Normal cast - Causes the rock to be shot out in a certain direction. Charging time increases the rock's initial velocity, dealing more damage and giving it the momentum needed to hit multiple enemies.

3) AoE cast - Causes an earthquake around the caster, knocking down nearby enemies and removing their handheld shield (if any). Also applies any additional magical elements effects to the area. Number of rocks increases area size.

4) Imbue - Causes a fissure to travel along the ground in a line, causing knockdown and applying effects like the AoE cast.

Spells containing Ice [QR]

Ice-based spells fire multiple small projectiles that deal damage to whatever they pass through based on their speed. Additional Ice elements increase the number of projectiles per shot. They ricochet off of shields and walls.

1) Self cast - Causes the projectiles to materialize above the caster and hit him on the head.

2) Normal cast - Causes the projectiles to be fired in the rough direction of the cursor. There is a high amount of spread. Charging increases velocity and decreases spread.

3) AoE cast - Causes large Ice spikes to rise up from the ground, dealing damage to nearby enemies. Additional Ice increases the size of the AoE and damage. Also applies any other elemental effects to the area.

4) Imbue - Causes the weapon to deal a high amount of piercing physical damage in an overhead swing at medium-long range. Ignores many types of defenses.

Spells containing Arcane [S] or Life [W]

These spells are typically thought of as "Beam spells" although in fact they only appear as beams when cast normally. They are often the spell of choice for new players, as they are fairly easy to conjure and aim.

1) Self cast - Applies a charge of life or arcane to the player, healing or dealing damage. Additional Life or Arcane elements have no effect.

2) Normal cast - Creates a beam in front of the player that will damage or heal. Beam spells can be crossed to increase their power, and reflect off of any shield surfaces. If any opposite elements are in two beams that cross, an explosion occurs at the point of crossing and both casters are flung backwards. Additional Life or Arcane elements increase beam duration.

3) AoE cast - Causes damage or healing in an area around the caster. Also applies any other elemental effects. Additional Life or Arcane increase AoE size.

4) Imbue - Causes a 90 degree swing in front of the player, applying damage or healing and any other elements included in the spell. Fairly short range.

Spells containing Sprays (Water [Q], Fire [F], Cold [R], or Steam [QF])

Spells of this type are often not very effective for damage, but apply dangerous status effects easily. They follow all the casting rules of Beam spells, except that the normal cast comes out in an AoE spray, wider but shorter range.

1) Water Sprays - Have extremely high knockback, no damage, and cause the targets to become wet.

2) Fire Sprays - Have fairly low damage, but inflict and extend the duration of "On fire" damage over time on any targets.

3) Cold Sprays - Have extremely low damage, but cause all dry targets to become chilled, which halves their animation speed, and cause all wet targets to become frozen, which prevents them from moving and triples any physical damage against them.

4) Steam Sprays - Have moderate damage, but cause any targets hit to become wet.

Spells containing only Lightning [A]

These spells cause mini-freezes to targets hit while they are being electrocuted and jump along a chain of targets beyond the original range of the spell. They tend to be short range and duration, although additional Lightning elements increase the range and duration slightly.

1) Self cast - Same as above.

2) Normal cast - Launches a bolt of lightning in the direction of the cursor which jumps beyond the first target if it hits anything.

3) AoE cast - Causes a very short range Lightning effect in an area around the caster, which can jump along multiple targets in multiple directions.

4) Imbue - Same as above.

Sources

Magickapedia - http://www.magickapedia.net/index.php?title=Spell_Combinations

This Steam Forum thread, old but somewhat relevant - http://forums.steampowered.com/forums/showthread.php?t=1733437

And many, many hours of personal experience.

There is a list of spells on the Magicka wiki. It's good for figuring out which ones you think you'll like. Mess around in Arena mode, testing out different spells and strategies. The most important thing is to remember which elements cancel out:

fire - frost
lightning - earth
arcane - life
water - lightning

which elements combine:

frost + water = ice
water + fire = steam
ice + fire = water
steam + frost = water

The last two are particularly useful, as they allow you to use water with elements that normally would not allow water, such as lightning. The casting system in Magicka is quite complex. It takes a little while to get the hang of it, but remembering the basics will allow you to create your own spells. I would recommend reading through the spell list, as it will tell you what each element does in each situation.

Some more useful reading is the Elements page, as it describes what each element does and how the combinations and cancels work.