Intro:
The skill descriptions show up differently on various devices, so trying to figure out what a particular skill actually does requires triangulation of all the descriptions for a single skill. Also, as I found with a Warrior, some skills have different benefits at different ranks, so what improves in later ranks might not be the same as earlier ranks.
Purpose:
For this reason I'm posting my own skill guide with screenshots from an iPhone. Hopefully this brings new information to light and will allow you to make more informed choices.
Definitions:
Aggro = Aggravation, i.e. which player the enemy is most angry with. If someone "has aggro" it means the enemy/enemies are attacking them. This is bad, unless you're a tank. Aggro is gained by generating Threat. Warriors can force aggro by using Taunt.
AoE = Area of Effect, in other words, this spell affects all targets within a certain area, not just the single target you have selected.
Buff = A spell that improves your/your party's stats.
Debuff = A spell that lowers your enemies' stats.
Threat = How much your actions are causing enemies to be aware of you. Actions that hurt your enemies or help your friend will cause threat; if you do a lot of damage (or healing) in a short period of time it will cause high-threat, and the enemies might aggro on you.
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Heal

Wait to put more points into this until you have Lightning maxed out, but don't forget to do it. Heal rank 5 is essential (each rank increases the amount healed). It is an AoE spell, so it heals all party members who are nearby.
Frostbite

Skip this entirely. It's single-target and the damage doesn't scale-up to make it worth having once you get AoE damage spells. You can do without this and just use a wand until you get Lightning (if the game still forces a point in this automatically, respec and remove it at a later point once you have a feel for the game).
Lightning

This is an AoE damage spell with a small armor debuff component. It's your second-best damage-per-second spell behind Firestorm and should be a staple of every Enchantress. Max it out right away (I recommend saving points ahead of time so you can dump as many as possible into Lightning as soon as you acquire it), because the damage increases with each rank.
Protip: The cooldown is quicker than Ice Storm & Firestorm, so you can usually sneak in 3 Lightnings in the same time you cast 2 Firestorms. Make sure you watch the Lightning cooldown and don't get locked in on cycling Ice Storm/Firestorm/Lightning in that order every time.
Resurrect

This will bring dead party-members back to life. It's an AoE spell (like Heal). When another player casts it on you while you're dead, you have the option to "Accept Revive", which will bring you back to life on the spot with low health and mana. This is what other players mean when they say "Rev plz" (they're asking you to cast Resurrect on them).
A note on Resurrect: The only listed improvement for extra ranks is a reduction of the mana cost. I've never had a situation where I had too-little mana for Resurrect, so it's currently pointless to invest more points in it. The developers should have additional ranks revive players with more health/mana, or temporary buffs of some type (extra armor, health regen, etc). That would make it actually worth having more than one rank.
Firestorm

This is your highest DPS spell, when combine with Ice Storm for a combo effect. Each rank increases the damage, so max this out ASAP (not before taking a point in Ice Storm, though). It is an AoE damage spell. There is also a small push-back component (not as big as Stomp), so it's not a good lead-off spell as it will mess-up positioning.
Protip: After you case Ice Storm, wait until you see the snowflakes form at enemies' feet before you cast Firestorm to ensure you'll get a combo. It's possible to cast Firestorm too quickly and miss getting the combo.
Ice Storm

This is an AoE damage/debuff spell. The primary purpose of this spell is to freeze a large group of enemies in place so you can combo-damage them with Firestorm. The damage per-rank only goes up slightly, so it's not worth increasing the rank SFAIK. It would be nice if additional ranks added crit chance to Firestorm combos.
Drain Life

This is a single-target, long-cooldown spell that will do damage to an enemy and heal you. You can initially skip this spell while you wait for Weakness, Magic Shield, and the Blessings. I came back to it in the low 30s because I was finding it tough to stay fully-healed while soloing. I noticed that the damage scales up really well with additional ranks, so even though it's a single-target spell it can be worth having, especially on boss fights.
Protip: Choose this over Nightmare (once you've maxed Weakness & BoM) if you solo a lot and/or don't play with very skilled players.
Weakness

This is an AoE debuff spell that drastically lowers the amount of damage and chance to hit by enemies in it's radius. You can tell you've hit because the enemies will have a purple star around their feet. I haven't tested how long the effect lasts, but the cooldown is short so when in doubt, recast. Every Enchantress should have this maxed IMO. It's really helpful when soloing to reduce the damage you take while waiting for your damage spell cooldowns. It's also great against bosses. Damage and hit% reduction increase with rank.
Protip: When your Warrior pulls a group with Beckon, cast this on the tightly packed group before you do any damage. It doesn't seem to cause much threat, so it's a safe opening spell.
Nightmare

This is a small AoE debuff that reduces enemies' armor and chance to dodge. This is a very helpful spell for Bears and Birds, but so far as I can tell provides no benefit to pure-INT Enchantresses. I solo a lot, so I don't find it useful. The radius is also quite small, compared to Weakness. I plan on maxing it out last. The amount reduced increases with rank.
Magic Shield

When you cast this spell, incoming damage is taken from your mana instead of your health for the duration. It's also a minor armor buff (to yourself). Initially I was excited about maxing this out, but then I realized the only apparent improvement per-rank is a small amount of additional armor. Since the cooldown time is fairly long, and the duration is short, you don't get to enjoy that armor very much, so it's just not worth it IMO to invest in extra ranks. Save your points for Blessing of Might.
Note: It would be great if the developers would lower the cooldown or increase the duration with additional ranks.
Blessing of Vitality

This is an AoE buff that increases max health nicely, and health regen slightly. The skill description is wrong (as sky../ pointed out): The short-duration self-buff is not health per second, it's extra armor. At rank 1 it grants 8 extra armor for 20 seconds (not bad). I do no know how much it increases per rank. This is a great spell to have (and use constantly), but additional ranks only improve the short self-buff, not the party buff (so far as I know).
Protip: Wait to cast this on the party until right before you go into a fight, that way you'll enjoy the health regen when the fight starts, when you're most vulnerable to taking a lot of damage.
Note: The developers need to fix the bugged description so it's clear what this spell does.
Blessing of Might

This is an AoE buff that slightly increases the STR and armor of your party. The real reason to have it is because it also grants a short buff to yourself that drastically increases damage and crit chance. The self-buff increases with rank. You should save points from skipping Nightmare and only putting one-each into Magic Shield and Blessing of Vitality to instantly max this out.
Protip: Try to time your recast so it happens just after the beginning of a fight (after the tank has established aggro), then pop BoM, Ice Storm, Firestorm (ka-BOOM!), Lightning, etc.
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Tactics
The biggest part of playing a pure-INT Enchantress is effectively using AoE spells. In general you want to round up enemies by making them follow you (with wand, running past them, etc), then freeze them with Ice Storm, combo with Firestorm, and follow with Lightning and debuffs as necessary. This allows you to hit as many enemies at once with your damage spells, causing a high amount of total damage per mana spent (and time spent). Your goal is to kill a high number of enemies quickly and AoE is the best way to do it.
It's not always best to lead off with an IS/FS combo. If you're in a party or soloing very tough enemies, you'll want to drop a Weakness as soon as you get them bunched-up. I often do IS/Wk/FS combo so the melee enemies can't hit me while I debuff them, but I still have time to get the combo damage. You might not even want to lead with IS at all. In really gnarly situations, use Weakness ASAP and focus on early Heals to the tank before you do any damage, which would cause high threat and potentially lead to you getting aggro.
Finally, try to train your Warriors how to use their skills to help you. Beckon is the #1 best Warrior skill, by far. At high rank it will suck in all the nearby enemies and draw them to the Warrior, thus forming a tight pack that is perfect for AoE. The Warrior should then Hell Scream to debuff them (which has a chance to stun at high rank), then Enchantresses should drop Weakness & Nightmare as appropriate, then do IS/FS combo. The #1 worst thing a Warrior can do is Stomp. This pushes all the enemies away, moving them out of the range of AoE. This makes Elves and Birds sad
(Vengeful Slash does it too, which is stupid. That Warrior skill should be changed).
(note, I have embedded the skill rank, character level, and INT total in the image name, so you can compare numbers fairly)
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