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6 tricks to start.
PRD:
Teach an Animal a Trick: You can teach an animal a specific trick with 1 week of work and a successful Handle Animal check against the indicated DC. An animal with an Intelligence score of 1 can learn a maximum of three tricks, while an animal with an Intelligence score of 2 can learn a maximum of six tricks. Possible tricks (and their associated DCs) include, but are not necessarily limited to, the following.
+1 bonus trick at 1st level (and +1/3 levels)
Rules text in question:
"Bonus Tricks
The value given in this column is the total number of “bonus” tricks that the animal knows in addition to any that the druid might choose to teach it (see the Handle Animal skill). These bonus tricks don’t require any training time or Handle Animal checks, and they don’t count against the normal limit of tricks known by the animal. The druid selects these bonus tricks, and once selected, they can’t be changed."
So at first level the druid's animal companion can know a total of 7 tricks. How many you let them start out with is up to you, however if you would let the wizard start with a familiar without paying for it you should probably let the animal companion have all it's tricks too.
For simplicity most DM's will allow you to treat the animal companion as a PC and let you run it which basically mean it will always do exactly what you ask it to i.e. no handle animal checks required.
it saves alot of needless rolling during combat if it simply does what you say it does. Noe if your going to do somthing unnatural or crazy with it the DM might get you to roll a handle animal check but simply to "go flank" or "act as mount" "charge" etc its just excessive dice rolling with no fun factor payoff
I remember the last time I play'd a druid I didn't even both tracking tricks , although I used their descriptions to improve how I ran the companion.