Is there an easy way to remember Invoker's spells?

Play this until you get your time down to 10 seconds or so: http://dl.dropbox.com/u/75495922/InvokerTrainer.htm

Then play a bot game or two until you're confident with your hero and your build, and you should be fine jumping into a real game at your skill level. The hero is definitely hard to play, but he's not nearly as hard as people pretend he is because he's so damned good at everything.

The skillbuild most commonly used right now:

QRQEEEREQQW

Q first for regen, R for Cold Snap, then another Q should give you plenty of regen in lane. Then you level E four times (getting Invoke when possible), followed by Q twice more. This puts you at 4-0-4-2, which allows you to summon double Forge Spirits as early as possible. This combined with Cold Snap is absolutely devastating at low levels- you will melt through armor and with three Exort orbs up you'll hit tremendously hard. From there you get a point in Wex to open up the rest of your spellbook (notably Ghost Walk). Typically you max E first, then W, to get the most casting power.

The typical item build:

• Starting items: Claw of Attack, Iron Branch, Healing Salve
• Early items: Phase Boots, then Drum, then Force Staff
• Midgame items: Aghanim's Scepter. You want to be finishing this right as you hit level 17.
• Luxury items: Sheepstick, Blink Dagger, Desolator, BKB, Eul's. All situational.

If you're interested in learning basics about the hero, I did a relatively popular walkthrough a few months back that goes over the old Quas-Wex build that was popular at the time. We didn't touch much on the Quas-Exort build that I've described above, though, and that QE style is much more popular recently due to a buff in the most recent balance patch. Video:

There is a flash game where you can practice and learn faster the combinations. The game is "Invoker" and can be found at http://www.invokergame.com/

Practice is always a great way to get the feeling of the gameplay

For me, I connect each spells to their respective elements;

Meteor : EEW : Major fire EE + travel W

Forge Spirit : Major fire EE + life essence Q

Sun Strike : Sun is pure fire so EEE

Ghost walk : Major cold QQ + slow travel W

Ice wall : Major cold QQ + Damage E

Cold snap : pure chilling power so QQQ

Alacrity : Major speed WW + Damage E

Tornado : Wind blast so WW + tornado is cold Q (I believe there's no hot tornado :))

EMP : Pure WWW just because it's less likely to mix up with another element than Tornado and Alacrity :D

You should give a try to our Invoker build creation page:

http://www.buildota2.com/build_creation?hero_name=invoker

Press the "?" button, set the desired level in one click and play with elements. You can level up core skills by clicking on them or simply press "Q", "W", "E" to level up elements and "R" to level up Invoke like it is in the game. Allowed abilities become colorful and you can get detailed information about them by tooltips. You can hold mouse over any ability and update the elements using keyboard to see how ability parameters evolve on the fly. Also you can fit any items to see how they update the Invoker characteristics as it is the common for all heroes feature.