Welcome to Ryze ADC. You may not have tried this before, and maybe I haven't either, but here goes the route to success! Prepare for the mind boggling unbelievably OP RYZE ADC.

For starting out, I suggest Can never go wrong with Doran's blade and this will prove some help with last hitting, sustain, and overall ability to survive.

On my first back, I tend to build these items.
Now if you're doing very well on first back, you can forget the Cloth armor and go for a first back such as this. However, the odds of having enough gold to go straight to one of your core items, the SHEEN are kind of slim. Same as your opponent's odds of victory versus the mighty AD Ryze!

Here are the core items and can be built in any order basically but most of the time you want tear of the goddess and warden's mail very early. It should be noted that tear of the goddess is an early game item and that this core build has more than six items and no boots! However any decent player should know that most of those items build into each other but for clarification sake, I'll do a more step by step approach.

Doran's Blade, Cloth Armor, Potions, Mana Crystal, Tear of the Goddess for longer games, Sheen if very far ahead, Then Sheen or Tear of the Goddess, whichever one you don't have, From here, you can go into the Warden's Mail, Zephyr, and other fun stuff. As far as boots are concerned, Tabi or Swiftness or Merc Treads and never Beserker's Greaves. Even though you are an ADC you are not relying on auto's but however exchanging trades with higher dps and therefore positioning boots or defensive boots will serve you well. A brutalizer is possible if the team is very smart and wise to the ryze as it provides some more punch to your attacks and gives that invaluable cdr and armor penetration. However, the fully upgraded brutalizer options are not all that great for AD Ryze. If you are having trouble with tanks, Blade of The Ruined King, is not a bad option. However, this should only be considered once in a while as most of the time you should be melting people with icebourne, zephyr, manamura, and frozen heart.

A work in progress, and will be flushed out later. Thanks! Ryze ADC works very well and is basically a Blue Ezreal, without the ****py early game! You will do very well as long as not faced up against a pesky Caitlyn or Ashe. Support nightmares are the one's with hard silence such as Soraka and Blitzcrank! Ban them unless you can get them on your team especially Soraka. She is one of ADC Ryze's best friends for obvious reasons although Sona, and a Lulu, are great as well and I guess Thresh since he is just a balling champion.

basically you're only options on OP AD RYZE!

Completely viable unless you're countered but the great thing about Ryze is he can go many other lanes. Ryze goes where he pleases.

Pro's

Super easy to last hit with
Amazing poke
Melting people in 1v1's
Melting people with splash damage
Burst Damage
Not having mana issues

Con's

Lack of range
No real escape
Weak versus casters
Usually no lifesteal
Caitlyn
Sivir
Ashe

Jungling is super easy as well as creeping as Ryze and many people jungle Ryze so winning the lane in creep score should never be a problem unless you are just getting melted by some annoying range character as listed above. Caityln and Ashe and Sivir is bad too because of her shield.

Ryze ADC is very valuable in team fights and with that frozen heart core build you last a litle bit longer in team fights and early game you are very helpful to the jungler with that snare. Snares for days!

Well Ryze ADC is unique in the fact that with his ultimate active he can heal himself for about 30% of base health and not too many ADC's have that kind of sustain on roughly a 20 second timer.

Try and see what you can achieve but I've never had problems farming as ADC ryze as you can suck at last hitting but still get them with spells.