All you need for starts. The mana crystal adds some nice 20 damage to your Overload, ensures you can spam it longer before you go back to base, and upgrades into your next item.
Health Potions will effectively give you free 400 bonus health. Self explanatory.
Tear of the Goddess
This is the first item you pick up. Even before the basic boots, if you dont have money for both. From the moment you get it, you get 4 max mana every time you harass somebody with Overload. Eventually it will become 1000 mana. One freaken thousand.
After Tear of the Goddess, you get your shoes. First the normal ones, than this. As you deal magic damage, those shoes will help you immensely.
Catalyst the Protector
Your next item after the shoes. This is where you start not only stacking mana, but also getting survivability along with it.
Upgrade your Catalyst into this. There the enemy teams ALWAYS have at least one caster, and/or some other characters with at some disables that'd focus you and tear you down.
In the extremely unlikely event that the enemy team has 3 or more AD carries, you can get this item as the last of your core items.
This item both gives you Mana, reduces your CD to nearly the max CD reduction, and... Survivability. Tanky Ryze, here we come!
Now you're really tanky. Not only that, but you also have huge DPS, never-ending mana pool, and your core items are completed. You're at your prime.
Here is the thing.. there are no more items that are as good for you as your core items. In fact, there is only one (!) item which is worth its price for you: The good old .
So what do you do?
I usually get 2 , and than upgrade them both into . More HP and Mana, that's all you need. You already melt faces without those items, but you can never get too much Mana.. Or HP.
Finally, if the game goes incredibly long, you can upgrade your into something (I wont enter this debate).
Do not get AP. I repeat, do NOT get AP. When you get AP, it's usually in the expanse of mana. Just get the items above, and be happy.
Early game (Mid)
Mid is where you like it. Ryze is a pretty level-dependent champ, since his Overload harass increases with the level, and so does his Runed Prison efficiency.
Anyhow, the strategy here depends on each hero. (I'll later update the guides regarding this, giving a detailed explanation of every mid opponent and hero in general, and how they interact with Ryze)
The rule of thumb here is - with most heroes, all you need to do is to hit them with as many Overloads as possible. Try not to spam too many at level 1, but be ready to spam every Overload you can starting with level 3 (lvl2 Overload).
Some, very few heroes are too tanky for you to harass (Example - Mordekaiser), so you should rather try to avoid their harassment skills and focus on pushing and last-hitting the enemy creeps, until you get your first items.
You should stay in your lane at least until you've farmed and . Once you did, you have a choice - proceed to the next step, or keep farming til you get and then proceed. (Btw, it'll take you at least 1 trip to base, than back to the lane, and back to base to get all the early items you need to farm).
*Note that if your mid opponent is a very good pusher, you should stay in the lane until either he teleports back to base or you kill him. Dont leave your lane before that, since you need your mid turret in one piece.
Once you're farmed enough, you do one of the following:
1) (Situational) Go get the BB golem if you have enough HP and Mana left
2) Teleport back to base.
3) Walk (or teleport, if it already isn't on CD) to one of your lanes, and set up a gank.
4) (Situational, if you killed both enemies and there is no one there to defend) Push the enemy turret.
5) (Situational) Farm a bit more.
6) Repeat steps 3-5 until it's mid game, and you got at least Banshee's Veil.
* Dont forget - if you see the enemy team pushing, screw the steps - you should always defend when your presence would make a difference.
* Try to have the blue buff as much as possible. You need the CD, and even more you need the huge mana regen.
* If you dont see any upcoming teamfights or ganks, use your Ulti to clear creep waves in your lane quickly, and heal while doing so. You can use it approximately every 2nd creep wave.
Early game (Solo lane)
Solo lane.. is definitely worse than mid. First, lets assume that it's a 1v2 lane, since if it's 1v1 your strategy is around the same as in what I've written above.
Before I talk more about the strategy on the lane, I'll tell you your goal there - your goal is to stay alive, farm as much as possible and eventually both outlevel and somewhat outfarm both your enemies.
It's important to say that you can not win most 1v2 fights, unless you somehow managed to get one of the enemies extremely low, to like 200 HP or so. That holds true until you're level 9 at least, and that's only in the best cases where you managed to do everything perfectly before that.
Now, what exactly do you need to do?
First off, do not attack the enemy minions except for last-hitting - you want to be as close to your tower as possible, to avoid being gibbed by both enemies.
Second, you should be harassing with your Overload, mainly once it is level 2 (harassing with it from level one will cost you too much mana, not viable against 2 opponents). Now, lets make one thing perfectly clear - you don't have any in-built HP regen, and HP potions can only help you so much. Avoid heavy enemy harassment, unless you're sure you'll do twice the damage with Overload. If one of the enemies has some easy means of regaining his health back, focus the other. Also, since you wont be stopping them from attacking your creeps, lifesteal will help them quite alot.
If they can't regen too rapidly, harass them as much as you can. If their regen is overwhelming, occasionally harass the less regenerating enemy, and kill him when your jungling hero comes to gank.
That's pretty much all you need to do. Stay on your lane unless some other lane drastically needs help (than you teleport there), otherwise don't leave it until you killed/scared off both your enemies, and destroyed the turret. By that time, you should have your first core item complete.
Early game (Dual lane)
You hate being here. Ryze thrives when he has the same or higher level than his enemies, which is not always the case if you're on a lane. Not to mention, in random games you'd be at the mercy of your lane mate, which has 50% chance of being a complete retard. But if you got stuck here, you have to get the best of a bad situation.
Unlike the old Ryze, the new one can do pretty good on the lane. You might not have any amazing AoE spells, but you still got a powerful Rune Prison and great harass in the form of Overload.
What you basically need to do is to harass the enemy, preferably the squishier one, with Overload, and try to kill him with your lane partner as soon as you can. Also, try to last-hit as much as possible - Ryze need every single coin he can get.
Remember to stay far enough from the enemies, as you're very squishy early on and you'll be killed pretty easily.
After the very long time, when you've finally gotten and , you can go gank to help other lanes. Your Runed Prison will help greatly. In case you've dominated your lane, you can push the tower first, than proceed to gank.
I can't write much about mid or late game, since those stages of the game are highly situational. The main thing that needs to be done during mid game is ganking, and using a successful gank to kill a turret and/or kill the Dragon (or late-game, Baron). I can, however, write more about your skill combo specifically, and about what you generally need to do during teamfights.
Well, the new Ryze is a "Magic Machinegun", as Riot said about him. He doesn't really have a one combo, since his skills allow him to pretty much spam spells. What you do is actually just spam your skills until yourtarget is dead, occasionally autoattacking.
Theoretically the combo with the highest damage on a single target would be:
Overload -> Runed Prison -> Spell Flux -> Overload -> Ultimate -> Autoattack -> Overload -> Autoattack -> Runed Prison -> Overload
This whole combo would take 10 second, some of which the target would be caged and some of which you'd be chasing it. Looks long? That's because Ryze doesn't have that much of a burst damage anymore, but rather high sustained damage. The short version of the combo is just Overload -> Runed Prison -> Spell Flux -> Overload. In this case, however, you're unlikely to kill any full HP target, even squishy, so you have to chase it down and turn it into something like the combo above.
Usually, people have to start their combo with Runed Priso, in which case it'd look like:
Runed Prison -> Overload -> Spell Flux -> Ultimate (or Autoattack) -> Overload -> ... Whatever comes out of CD, up to the point your target dies. Note that with max CD reduction, you'd usually get Runed Prison off CD again at this point, right after another Overload.
The skill combos for multiple opponents are about activating your ulti, so that's around how they look:
Overload -> Ulti (While Overload still flies) -> Runed Prison -> Overload -> Spell Flux -> Autoattack -> Overload -> ... Well, and spam whatever comes off CD to finish your enemies.
*You don't really need to remember any of the whole above combos, since after the first 3/4 spells you pretty much use everything that comes off CD. Once you have enough experience with Ryze, spamming skills will come naturally.
Golden Rule: Use Overload whenever you can for damage, Rune Prison for chasing, all other skills to lower the CD of the first 2.
*In late game, your ultimate can sometimes help you survive enemy focus though. Use it wisely!
In teamfights, your got 2 jobs: The main job, which is DPsing down the enemies, and the second job, which is snaring that 1 enemy that either comes too close (can also be used to initiate the fight) or snaring the one which depend on mobility (some melee DPS carry).
While certainly need to try to DPS the squishiest enemy, don't forget that the other enemy team will focus you quite a bit, so don't get out of position. Once you get more tanky, you can try to get that 1 low HP enemy that you know you can finish, but not initiate on their squishy carry who stands behind the whole team. You still have to remember - even with ~100 magic and ~180 physical armor, you're still not a complete tank; You may be tanky, but real tanks can take 2 times as much as you can, and you cannot survive a focused assault from 3+ enemy champions, even if they're half as farmed as you.
In short, once the teamfight has started, you usually run around nuking the squishiest hero you can get to without getting out of position. Once you have enough experience playing Ryze, you'll learn to position yourself better and better - this isn't something you can learn from a guide.
Anyway, that's pretty much everything I can write about Ryze.
Hope this guide has helped you, or will at least help you soon.
Now go out there,get some mana , nuke some dudes and win some games!!!