Talking to the Progress Hat will tell you how many points you have in the different areas. In each of the areas you will gain so called "Pizazz points", which are categorized in four kinds, each corresponding with the arena where you gained them.
For all those who love to cut down Magic Trees, there are 2 outside the Arena! Also, random events do NOT occur while in the arenas!

Fire and Nature runes, Level 21 Magic

Recommended:

Fire staff/battlestaff/mystic staff, at least 100 Natures

The goal is to get items and alch them for money and Pizazz points. In the top right corner it shows a small menu with the current values of the items.

NOTE: These change constantly! Search the eight cupboards for items. The items are in order as stated in the list on the right side of your screen. The items in the cabinets are going clockwise. They just change their starting spot. The three "empty's" are clumped together. So, once you find an item, you can quickly determine where the 30 gp item is:

If you're not using a fire/lava staff, I recommend low alchemy, since you get the same GP anyway, although this will reduce your experience gain.

• Now alch the item indicated by the arrow or is worth 30 gp. You will then receive coins.
  
  
• The number of coins you get is indicated in the small list in the corner.
  
  
• So items don't give their normal high alch value.
  
  
• Try to alch the items which are indicated by the arrow or are worth 30 coins.
  
  
• For every 100 coins you will receive 1 Alchemy Pizazz point and 200 magic Exp.
  
  
• Try to deposit in sets of 100 coins, otherwise you'll lose out. E.G. 1st time you deposit 199 coins, you'll get 1 point and 398 Magic Exp. 2nd time you deposit 1 coin. Now you don't get any points, although you have deposited 200 coins in total, the game counts only sets of 100! So deposit your money often. If you log out with gp in your inventory, you will lose it.
  
  
• Be a sport and call out "HERE!" if you find the cabinet worth 30 or has green arrow. Encourages teamwork.

Strategy:

Bring in 4 or 5 natures (So if you mess up you have 4 extra chances) and stash a load of about everything inside the cupoards. Stand by the alchemy guardian and wait for him to say "X can now be converted for free".

NOTE: The item indicated by an arrow can be alched for free! High alch DOESN'T give more coins than Low alch. I hear some of you think: "Oh, I'll just take a few k into the arena then! Easy points!" Your problem is, you can't take money into the arenas.

Law and Air runes, Level 33 Magic

Recommended:

Air staff/battlestaff/mystic staff, at least 100 Laws

The goal is to move the statue through several mazes with Telekinetic Grab. The statue moves according to the angle you stand with it. E.G.: If you want to get the statue to move left. Go to his left side wall then use telekinetic grab on him. The statue moves until it hits a wall. If you press observe statue you will get an overview on the arena.
Each maze uses 7-10 law runes. After completing a maze, talk to the Maze Master, and he shall teleport you to the next one. Completing one maze will earn you 2 Telekinetic Pizazz points. Completing five mazes in a row will conclude in gaining an extra 1k Magic Exp, a bonus 8 Telekinetic Pizazz points and 10 extra Law Runes.

Cosmic runes + runes to cast any of the Enchant Jewelry spells.

Recommended:

Staff/battlestaff/mystic staff of the type of the highest enchant spell you can do, at least 100 Cosmic Runes.

The goal here is to get shapes from each of the corners and convert them into orbs with the Enchant Jewelry spell. You will get a bonus point for Enchanting the colour which is indicated in the lower right corner. After ten enchantments, deposit the orbs in the hole in the center of the chamber. You'll get 10 points for every 10 orbs deposited in the hole. So you DON'T get 1 point per orb deposited, only per 10!

Locations:

Cube: north-west (1 iscosahedron pile)
Cylinder: north-east (1 pentamid pile)
Iscosahedron: south-east (1 cube pile)
Pentamid: south-west (1 cylinder pile)

You'll get an extra 5 points per 10 orbs deposited. Sometimes, dragonstones appear. Enchanting these will result in gaining extra Enchantment Pizazz points, depending on the spell used:

The dragonstones CANNOT be alched and cannot leave the arena. So dont get any ideas.
NOTE: All experience gained in the Enchantment room is been decreased by 25%.

A Strategy:

Some rooms have 2 shapes by each other. Stand in between and wait for one of the two bonus shapes to show up. Best way is get 13 of each item if you have inventory and wait for bonus to show up. You save 50% of your time doing this, if not more.

Another Strategy:

Switch between the two northern spots. So, what I do usually is pick up 9 red, 9 yellow, and 9 blue (Substitute green in there.) and wait for the bonus to show up.

NOTE: If you log out while INSIDE the arena, you only get your bonus points, not any other points you have earned by making orbs! So always exit the arena before logging out or answering the phone or anything!

Nature, Water and earth runes, Level 15 Magic.

Recommended:

Mud battlestaff/mystic staff, 100 Natures.

Your goal is to convert the constant appearing bones into, yes finally a use for it, bananas! Converting bones will earn you Graveyard Pizazz points.
Different levels of bones give different numbers of bananas. The bones are on the side of your screen, each numbered 1-4. Level 1 bones give 1 banana, Level 2 gives 2 bananas, etc etc. Try to get a spot near both a deposit and a bone spawn.
After aquiring the Bones to Peaches spell, they heal more health, and give more points than bananas do.
You sometimes get hit by the bones, so you may wish to eat some bananas yourself! The remaining bananas can be deposited in the Food Chutes around the chamber.
NOTE: If you die, the ONLY thing you will lose is 10 Graveyard Pizazz points, not anything else!

A Strategy:

Don't look for good bones, just pick up 12 bones, cast and deposit. Go fast, and use nurses at Duel arena to heal you back.

Another Strategy:

Pretty easy. I bring 5 lobbys in, and go to a bonepile near the deposit. I found out if you can register math pretty quickly, and recognize the bone stacks that you can actually do this REALLY fast. Bones give 1, 2, 3, and 4 bananas. If you get a 4 color bone, thing 4 in your head, another = 8, another = 12, then 4 normal bones = 16. Think about it and youll usually get REALLY close. Bone level is probably the easiest level. DONT EAT the arena bananas though, eat your own good fish. Cakes work too.

The cost is Telekinetic + Alchemy + Enchant + Graveyard Pizazz points:

*NOTE: Each new wand is an upgrade for it's predecessor, so you need to have an Apprentice wand to get a Teacher wand.

**NOTE: All wands have NORMAL autocast options, so no Ancient Magicks.

Post Guide NOTE: For all those interested in Magic Exp, do the Enchanters' Chamber. Cosmic Runes are quickly available in Runecrafting and don't cost a lot.