Your item sequence could be the most important part during a match other than your raw skill and intelligence. Starting off with a Health Pot and 2 Mana Pots, along side with Boots of speed. Work on farming some starting gold and slowly working down your enemy champions health to about 1/3. This will prevent the enemy from leaving to go heal. about level 5 you should be able to kill the enemy easily at his 1/3 health. Doing this by your Combo - Cast overload, Rune Prism, and Spell flux (IN THAT ORDER) almost simultaneously. Then overload should be cooled down by then allowing for 1 more additional finishing strike.

Your combo with Ryze is one the most deadly combos if used correctly. Work on your timing of when to attack and when you should be casting. Since everytime you cast a spell, it reduces cooldowns for your other spells, Casting heavily in higher levels gives you an upper hand.

Combos such as:
R-Q-W-E-Q
or Work very well and are very powerful.
R-Q-W-Q-E-Q

One little tip, when you've baited your enemies health down and want to use your ultimate combo, allow them to use their 'Ignite' spell or whatever hard hitting ability they have on a Minion first. So you don't take that damage and you can swoop in while they're off guard from the previous spell to finish them off.

Start off with a Health Pot, 2 Mana pots, and boots of speed. Depending on how much you're able to make, either buy Tear of the Goddess OR if you have enough go straight to Archangel Staff along with Sorcerer Boots. Save up next for Catalyst the Protector and then upgrade to Rod of Ages. Purchase a Blasting wand, and a Needlessly Large Rod. Upgrade that to the Rabadon's Deathcap. With these, you should be strong enough to take down even the mightiest champions with close to 1/5 health. With 2 spots left, I leave for a good Health Regen item- which I start by getting the Philosopher's Stone and upgrading to Shurelya's Reverie. Leaving 1 item spot I like to fill with more Ability Power. I go for a good/cheapER item - Void staff. Which in no hurry to get by this point, just for added power if needed for long matches. With really long matches or if you're able to farm gold well. Replace with another Rabadon's hat or whatever your interests are.

Runes can be laid out to which ever way to prefer. And as for me, I don't even pay attention to them that much because even though they help, its not the 'Game-changer'.

Masteries also, bare only some additives during a round but nothing too noticeable. So where ever you feel comfortable putting them.

If you don't think this looks like a good guide, I don't see how you can't agree with 3k health and 5k mana as a weak mage at level 18 with devastating power.

If you have any questions or comments please leave them, kindly.
-I am working on putting a video together to go with this thread to maybe help understand the way I play and how well it works for me.