What can a new commercial pilot do to build flight time?
For a commercial pilot (without a CFI rating) you've got some options, but the real golden goose of time building is flight instructing. Most folks I know who are time-building accumulate the minimum amount of time until they have enough to get the CFI rating, then go out and instruct to get to their end goal (time / types).

Without the CFI rating, some things to look in to include:


Banner Tow (if available in your area)
Crop dusting (again, if available in your area)
Glider towing 
Skydiving
The FAA has a page on skydiving operations this that's worth a read.
Ferry Piloting (if you don't mind the travel)
Photo work - anything from costal erosion photos to event coverage depending on your location.
News work - Hand in hand with Photo work, but also traffic and the like.
Sightseeing flights
AOPA has a page on this which is worth a read, take care as you almost certainly want to be sure you fall under Part 91 and not Part 135!
Deliveries.
Someone needs a wedding cake moved across the state? You can often do that in a Cessna more efficiently than they can by car, and as a commercial pilot you can even charge for it.
Corporate Flight Jobs  
Sightseeing within 25sm of an airport


There are some outfits that will "sell" you SIC in their cargo twins. It's a way to build TT, but it's considered an unscrupulous practice. 

Many of these will probably require the very time you're looking to build, or experience in specific types of aircraft, but it can't hurt to investigate.