Some chases may occur in a localized area and are fast-paced like a chase scene in a movie. As described in Quentin's answer, there are rules for designing chases like obstacle courses, typically resolved by a series of d20-based tests; these could consist of skill checks (such as Acrobatics/Climb to get over obstructions), or sometimes even saving throws (such as Fortitude to get through a smog-filled hallway). In a sense, this is a contest between the pursuing party and the fleeing party, to see who is first to pass all of the obstacles.
Spells that increase movement speed will give the pursuers an advantage. Spells with durations of rounds or minutes per level are probably sufficient, since these chases tend to end relatively quickly. Haste is a great option for a group of pursuers. In addition, the pursuers could slow the fleeing party by creating new obstacles, such as difficult terrain (e.g., Entangle), solid objects (e.g., Wall of Stone), or dangerous hazards (e.g., Create Pit).
Chases may be different when traveling long distances, over an extended period of time. Maybe the pursuers started far away, or the fleeing party had a head start. If the party is traveling together, then you use averages and approximations for the party speed, rather than individual character speeds. Pathfinder's movement rules have a table for getting these numbers. Like you mentioned in the question, this is where tracking and terrain familiarity can give some speed benefits.
To gain more effective advantages, the pursuers have a variety of options. For spells, their most effective magical options have durations of hours or days per level; Overland Flight is an obvious choice for multiple pursuers. Or, they could cast minutes-per-level spells like Mass Fly multiple times per day, which may save them time in the long run. Or, they could avoid the problem entirely and Teleport instead. And if they don't have spellcasting means, they could simply purchase a group of mounts (such as horses) that have faster land speeds.