Let's say you have a Cleric 1/Sorcerer 2/Mystic Theurge 5
Early entry because the Cleric has Trickery domain and gets a 2nd level SLA from being an Aasimar, details, whatever.
So, your available spells and slots are (ignoring bonus spells from high stats)
Cleric (Caster level 6) Spells prepared:
Level 0: Detect Magic
Level 0: Guidance
Level 0: Light
Level 0: Create Water
Level 1: Remove Fear
Level 1: Sanctuary
Level 1: Divine Favor
Level 1 (domain): Disguise Self
Level 2: Bull's Strength
Level 2: Hold Person
Level 2: Consecrate
Level 2 (domain): Invisibility
Level 3: Blindness/Deafness
Level 3: Prayer
Level 3 (domain): Non Detection
Sorcerer: (CL 7)
Level 0 Known: 7 spells, whatever
Level 1 Known: (5 spells) Mage Armor, Magic Missile, Comprehend Languages, Shield, Burning Hands
Level 1 slots: 6
Level 2 known: (3 spells) Glitterdust, Web, Touch of Idiocy
Level 2 slots: 6
Level 3 known: Fireball, Dispell Magic
Level 3 slots: 4
As a Mystic Theurge, the character has several options:
1.) Cast the spells as if he were a multi classes Sorcerer/Cleric: Just cast Cleric spells from Cleric slots and Sorcerer spells from Sorcerer slots. Nothing special to see here, move along.
2.) Cast Cleric spells out of Sorcerer slots.
2.a) It costs a spell slot one higher than it would cost to cast it from the appropriate class's spell slots.
2.b) The spell has to have been prepared that day, but could have already been cast.
2.c.) The spell uses the Sorcerer's casting stat for saves and caster level, but the original spell level to calculate saves.*
2.d.) Example: The character has plenty of Sorcerer spell slots, so he decides to save a Cleric slot and cast Remove Fear by expending a second level Sorcerer slot, leaving him with 5 left for the day instead of 6. Or, he has already cast Hold Person from the Cleric slot, later in the day he comes across a situation where he needs a little control, so he expends a 3rd level Sorcerer slot to cast Hold Person again, which would last for 7 rounds and have a save DC of 10 + 2 (Spell level) + CHA.
3.) Prepare and then cast Sorcerer spells out of Cleric slots.
3.a) It has to be a spell known from their Sorcerer class.
3.b) It has to have been prepared as a normal spell, it cannot be cast spontaneously.
3.c) It takes up a slot one level higher than the "normal" class would use.
3.d) The spell uses the Cleric's casting stat and caster level, but the original spell level to calculate saves.*
3.e) Example: The player doesn't like second level Cleric spells, so when he prepares spells for the day, he prepares Shield instead of the Divine Favor I have listed up there, which would last for 6 minutes because his Cleric caster level is 6.
* Note that I am not 100% certain on what level the spell is considered, I think it's a bit of a grey area. Generally things that raise the level of slot a spell uses don't affect its save, but it isn't specified either way in the MT text. So, table variation as they say in PFS, but I think the general rule is that casting from a higher slot doesn't raise the level as far as saves are concerned.
