Fleeing an encounter is difficult in Dungeons and Dragons, Third Edition
Tactically, a creature wanting to end an encounter moves away, usually by taking the action run (Player's Handbook (2000) 127) or double move (PH 126–7). Running is straight-line-only movement of typically 4× the creature's speed but causes the creature to lose its Dexterity bonus to Armor Class and does nothing to obviate any attacks of opportunity that the creature may incur due to its movement. A double move, on the other hand, is safer but slower, allowing the creature to move up to twice its speed and the creature doesn't provoke attacks of opportunity for leaving the space it started from. (Also see Movement on PH 117).1
Likewise, tactically, those who wish to pursue do so by going after the creature, also usually taking the action run or a double move or, if within striking distance, by taking the action charge (PH 124), ending the charge with a grapple attempt (PH 137). Success on the grapple attempt means grappling ensues, and the formerly-fleeing creature's progress is halted unless it escapes the grapple.
This all occurs on the grid or battlemat or whatever playing surface you're using, by the way. Make some room.
Strategically, the Dungeon Master's Guide (2000) provides frankly pretty terrible (albeit nominally realistic and certainly playable) rules for Evasion and Pursuit (70). To summarize, the faster dude wins, yet if speeds are equal make opposed Dexterity checks, with the winner succeeding either in catching up or losing his pursuers, as desired.2
1 This free-space-during-a-double-move idea would later be codified by the 3.5 revision into the action withdraw.
2 If you want more interesting narrative chases, the sort-of D&D 3E compatible Pathfinder Role-playing Game makes its chase procedure available here.