Let’s say my BAB is +6/+1.
I am using a spiked chain.
I have the feat Improved Trip.
Can you walk me through the process of a trip attack, or possibly attacks, if I use a full round action to trip+attack? (Or only one, if there is no benefit.)
These attack forms [that include trip attempts] substitute for a melee attack, not an action. As melee attacks, they can be used once in an attack or charge action, one or more times in a full attack action, or even as an attack of opportunity. (141)
For example, Amy is a human fighter 6. She possesses Strength 10, wields a spiked chain (PH 115, 117) (25 gp; 10 lbs.) with which she is proficient, and possesses the feat Improved Trip (PH 96). Amy has no other abilities or gear relevant to this example. (Let's not judge, okay?) When Amy takes a full-round action to make a full attack her turn looks like this:
Amy makes a trip attempt against a foe within her spiked chain's reach. She makes one touch attack with her spiked chain at her full base attack bonus. Note: If Amy lacked the feat Improved Trip, her foe—were Amy within the foe's threatened area—could make against her an attack of opportunity, striking Amy during the trip attempt; however, unlike making a grapple attempt, the foe's successful attack if typical (i.e. solely dealing damage) won't prevent Amy from continuing to make the trip attempt. The foe can't made this attack of opportunity if Amy's outside the foe's threatened area. Amy makes her trip attempt from her space; when she attacks she does not, like, lean out of her space and briefly occupy another space!
Success means that Amy continues the trip attempt process.
Due to Amy having taken the full attack action and her high base attack bonus, Amy can now make a second attack at her base attack bonus −5. If this is another trip attempt, restart the process except that Amy's initial touch attack suffers a −5 penalty and that, if Amy renders a different foe prone, the attack bestowed by the feat Improved Trip will also suffer a −5 penalty. (While some creative lawyers may argue otherwise, most agree that an already prone creature—or one not yet fully standing and, instead, in the process of standing up from prone—can't be tripped again.) Were Amy to have a third attack due to a high base attack bonus, she could restart the process a second time with the penalties at −10, and with a base attack bonus of +16 or higher even restart it a third time yet at −15.
The core rules don't actually mention what happens on a tie during a trip attempt (despite doing so on a grapple check made to hold, for instance, the winner being the creature with the higher grapple check bonus), and neither does the Rules Compendium (145). This DM has always assumed that because the attacker didn't win that a tie should go to the defender, but this DM's opinion may be colored by his hatred of trip attempts. Another DM's opinion may differ (for instance, another DM may take a page from the grapple special attack and declare the winner the creature with the higher opposed trip check bonus).
Also keep in mind that the Rules Compendium would seem to have the countertrip attempt use all the standard rules and modifiers for tripping. In its entirety the Rules Compendium on countertipping says, "If you lose, the defender can immediately react to try to trip you," therefore implying one follows all the rules on tripping that the text provides. This DM prefers the core rules' elegance.