There are essentially two types of billing for contract work: Fixed Bid or Time & Materials. Both have their advantages and disadvantages. And you’d better know up-front which one your client has in mind before you start talking about money.
A Fixed Bid contract is just like it sounds. You bid that you can do a defined set of work for a fixed amount of money. If you are more efficient at doing the work, you make more money per hour of work done.
If you are inefficient, or worse, overlooked something about the project (or you allowed scope-creep), you can spend a lot of time and end up bringing your effective rate per hour way down, possibly even losing money on the project if you really blow it.
A Time & Materials contract is similar to being an hourly employee, at least in that you are paid a set rate for the actual hours that you worked, and you may be reimbursed for specific expenses such as hardware that you purchase for the company.
You don’t work, you don’t get paid (see my notes about unpaid holidays for more on this). If you are efficient, you might make less money overall, but if scope-creep enters in, you still get paid for all of your work. (Scope-creep is when you allow the defined set of boundaries for the work to be expanded. A telltale sign this is happening is when you hear someone say, As long as we’re doing that, let’s….)