Early Game

Ryze is a challenging champion to play early game, but will really shine mid/late game. Early game your mana pool will be quite low, so use it efficiently! Wait until minions are low and use your auto attacks to secure your last hits, only use your ability's for the few minions that your attack speed can't keep up with. As soon as you have enough gold find a chance to recall and buy your Tear of the goddess, now you can safely spend mana on securing cs without constantly finding yourself out of mana!
PROTIP: your tear of the goddess gives +4 maximum mana per ability cast (3 second cooldown) both your tear and your Overload (Q) have similar cooldowns, so make sure your constantly pumping out Q's! Since Ryze's ability damage scales off his maximum mana this means you will constantly be gaining damage!
REMEMBER ability casts during the items cooldown will refresh the cooldown with no mana gain, so make sure your ability casts are timed with the items cooldown. (this is only for cs'ing)