Old ryze was a very squishy nuker with low spell-range, oldold ryze was a demaciaaa (cit.) caster OMG1SHOT on brush with flux, now what is ryze? Atm he is a [highlight]tanky mage burster with good resistance, very low cd and good range[/highlight] that make ryze the most mage spammer of lol. He's mana-based champ, ap is pretty useless with his low ratio; mana provide dmg (Q-W) and a large pool to spam skill.
[highlight]Ryze dmg source is mana[/highlight], not ability power. His skill ap ratios are low and bonus dmg from mana is very good ([number]10%[/number] on Q, [number]5%[/number] on W). Therefore a good choice is boost mana with seals/glyph/quint, this spec provide about [number]640[/number] mana at lv 18 (64 dmg+ Q, 32 dmg+ W). Without hp quint you will start with poor hp ([number]440[/number]~) and this make your early game very hard (probably you'll need jungler help for first recall).
Overload is your primary source of dmg, good output and very low cd. Snare is your second priority, take 1 point on E for debuff mres and reduce cd during combo. If you need more snare (rare case) you can up W first (in TT lv 1 snare can be better).
Combo is a basic part of ryze knowledge, his passive is wonderful and you will maximize its utility with combos. There are many way to spam skills, i'll show you the most important combos. [highlight]Basic combo to maximize dmg output (useful in 1v1)[/highlight]: [img=skills/ryze/q.png][img=skills/ryze/w.png][img=skills/ryze/q.png][img=skills/ryze/e.png][img=skills/ryze/q.png][img=skills/ryze/r.png][img=skills/ryze/q.png][img=skills/ryze/w.png][img=skills/ryze/q.png][img=skills/ryze/e.png][img=skills/ryze/q.png] This combo maximize dps on single target (it's possible make some autoatk too, usually after cage [Q-W-atk-Q-...]) [highlight]Aoe dmg (useful in tf)[/highlight]: [img=skills/ryze/r.png][img=skills/ryze/e.png][img=skills/ryze/q.png][img=skills/ryze/w.png][img=skills/ryze/q.png] This combo make fast aoe dmg in tf if target is near his team (E to debuff mres). [highlight]More snare combo (useful if jungler/team coming and you need snare enemy to wait help)[/highlight]: [img=skills/ryze/w.png][img=skills/ryze/e.png][img=skills/ryze/q.png][img=skills/ryze/r.png][img=skills/ryze/w.png] You need spam your other skills to reduce prison cd. [highlight]Last hit combo (usually flash + combo with low life enemy)[/highlight]: [img=skills/ryze/w.png][img=skills/ryze/e.png][img=skills/ryze/q.png][img=skills/ryze/r.png][img=skills/ryze/q.png] Flash + snare, E to maximize Q, R and another Q. There are other combinations of skills, your first source of power is your imagination and elasticity, use combos to regulate your cd and maximize utility from time to time.
Mana stack is really basic to play ryze, so you need [highlight]tear[/highlight] for mana pool, regen and increase max mana = dmg output. [highlight]Catalyst[/highlight] is good for hp and mana (wonderful passive for laning) and you will turn it into banshee. In fact, every item with good mana is wonderful on ryze, so [highlight]stacking defensive item[/highlight] like banshee or frozen (basic for cap cd red) is the way to make tanky mage ([number]180[/number] armor, [number]80[/number] mres) with tons of magic dps. Why manamune as alternative? simple answer: [highlight]less time to stack and better tower pushing[/highlight]. Manamune increase mana pool even with autoatk so you will stack it faster than arch (and phys dmg isn't useless, with [number]6k[/number]~ mana at end build you'll gain [number]120+20[/number] dmg, not bad). Arch provide ap too and give you a lot of dmg at full stack, so decision is hard, manamune give you dmg faster and phys dmg, arch give you more magic dmg. Roa is usefull too to increase hp and mana. Sixth item is very situational, you can buy some defensive item like fon (ms is really good too) or randuin, or buy offensive item and here there are many choices. If you had take manamune, trinity force can be right choice to make really good phys dmg during combo with improved ms, crit and possible slow, if you had take archangel you can take lichbane, if enemies stack mres you can take void, even another roa can be a good choice to maximize mana.
Sapphire crystal start make your [highlight]early game very hard[/highlight], especially versus high harasser ([number]90%[/number] of midders), then be care, last hit with autoatk and farm gold to tear, recall (jungler will take mid) and now you can make something. Tear provide you dmg, pool to spam and max mana every skill for other dmg, so last hit with Q every time (but keep some mana to snare ganker) or harass enemy if he's weak (you can try to kill low life enemy with flash last hit combo but it's better keep flash for gank). You need [highlight]farm and farm[/highlight] (clear lane with R + combo before recall), stack tear and make gold for catalyst and boots, after these items you can really make serious dmg and easy gank on other lane (you aren't a good pusher so gank lanes instead of push tower when the lane is clear). Mana is your priority so spam every time you can to stack manamune (or archangel), gank and keep in mind your combos, maximize your cd is basic to play ryze.
Last patch changed completely ryze, made him very fun to play and more difficult to use too. Elasticity, imagination and creativity is your weapons with this tanky mage, so... [highlight]can you handle this?[/highlight] (cit.)