The Fireball spell does 1d6 die of damage per overall caster level up to 10d6 at the caster's tenth level.
She should roll 10d6 for her fireball damage.
The caster level for a spell is determined by the player's overall caster level.
A caster level is a character level taken in a character class that gains caster levels at a level and rate defined in their class description. See the rules on pg 171 of the PHB under the header CASTER LEVEL, and under each class that can cast spells.
For a straight up Wizard, Fireball Dmg starts out at 5d6 when you get the spell at a Wizard and Caster level of 5th, and, assuming you take your next level in Wizard, it goes to 6d6 because you gain another caster level with that Wizard level; 7d6 at 7th, etc. This continues all the way up to 10d6 at the 10th caster level where it caps out. Further caster levels gained will not increase the dice of fireball damage.
From the 3.5 PHB pg 231
A fireball spell [...] deals 1d6 points of fire damage per caster level (maximum 10d6) to every creature within the area.
Whenever the rules say "per (x) level" you can simply multiply by the number of relevant character levels of (x) to get the desired effect. In this case it states "per caster level" so you would count only character levels the PC took in the class that they are using to cast this spell (and any classes that specifically stack - see prestige classes in the DMG, pg 176 for starters) - and that is the number of d6 you then roll.
NOTE: This is for 3.5 rules. Things can be much different in other editions.