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When multi-classing spell casting classes designate one of the classes as your primary caster class. When determining your spells per day add all of your levels in your spell casting classes together and look on your primary class' spells per day chart then subtract your secondary spell casting class’ spells per day from that.
So a level 10 character that is primarily a sorcerer (7th) and secondly a cleric (3rd) would have the following spells available per day.
Sorcerer
4 (=6-2) /5 (=6-1)/6/5/3 (Spontaneous casting with sorcerer spells known) (may not convert to healing / inflict spells)
Cleric
2+1/1+1 (Must be prepared in advance via cleric spell list and may spontaneously convert them to healing / inflict spells)
They would have all the class abilities of a 7th level sorcerer and those of a 3rd level cleric and a caster level of 10.
Bards only add .75 of a caster level per level of bard (rounded down). Paladins, and Rangers only add .25 of a level rounded down.