If playing solo, it's best to run ahead of Joseph to clear the way of zombies to reduce the risk of him dying.
If you know the route Joseph will take you can clear it just before taking the mission to make things easier. In Patch 1.3 he heads south, jags east to go around the Quarantine zone, passes west of the Warehouse/Simon's Hub, and then jags west through the center of the market. He will stop at the vendor south of the Warehouse to pontificate about greed (good chance to buy/sell, especially in single player, stay a little away from him and he'll wait so you can do other things like unlock Simon's Hub if you haven't or place a poster as part of a side quest). After passing through the open market he turns west and crosses through the river just north of the bridge/road. He enters the waste treatment grounds on the northeast corner and heads to the southwest (the sewer entrance). Earlier versions of the game had him following a different path.
Get your reward from Joseph before entering the sewers; after that point, he won't pay you. Actually grab it as soon as it's offered. On Patch 1.3 there is a small window of time (roughly 1 second) before he stopped offering it and moves on to offering the next section of the quest. This quest ends in the forested area in the middle of Moresby (the sewage treatment plant) and there will be Walkers around when you get there so stick close to Joseph if you want the cash.