Finding a Borgia courier is half of the challenge; catching him is the other half.
To find him, look for an unidentified man running around with a white arrow indicator above his head. There will be no icon on your map or minimap. I first found one in the Santa Maria Novella section of Firenze (Florence).
Once you find one, chase him down. In order to "intercept" him, you'll want to lock onto him with the left trigger and then tackle him using the B button (you can also attack/assassinate him by pressing X). He can be a little tricky to catch, as he's quite fast and travels over rooftops, but if you use the free running sprinting whenever you can, it won't take too long to run him down.
If you succeed, you'll earn (steal) approximately 1500 florins. If you tackled him, he'll beg for his life and run away; if you killed him, you'll become notorious and be chased by guards (if any are nearby). The achievement pops as soon as you tackle/kill him.