It's a big part of being a commercial pilot...

1) Four Elements

Common carriage can be described as (1) holding out of a willingness (2) to transport people or property (3) from place to place (4) for compensation or hire.

2) Holding Out

This is essentially you advertising your services as a commercial pilot. Unless you fall under 14 CFR Part 119 regarding air carrier operations, you're not allowed to hold out as a commercial pilot. For example, offering your friend a ride from Point A to Point B for compensation or hire isn't legal.

3) Part 119 Exceptions

FAR 119.1 (e) lists jobs that don't require you to have a 135/121 certificate. These jobs include flight instruction, banner towing, crop dusting, aerial photography, etc.

4) Wet Lease

A wet lease is considered to be an operation where both the aircraft and pilot are supplied by the same company. For example, an FBO providing an aircraft and a pilot to fly an individual from Point A to Point B. Unless you have an air carrier certificate, this is not legal.

5) Dry Lease

A dry lease is when the pilot and aircraft come from two different sources. However, there's more to it than a few sentences can describe. Read more about it here and here.

6) Pro Rata Share

Even with a commercial pilot certificate, unless you fall under the exceptions of Part 119 (e) or operate as a commercial pilot for an air carrier (121 or 135), if you plan to share the expenses of the flight, you must 1) not pay less then the pro rata share of the operating expenses and 2) you and your passengers must have a common purpose for the flight.