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...”.)

On almost every project I have ever worked, the manager will ask for an estimate before agreeing to have you do the work.  It is ABSOLUTELY CRITICAL that before you provide an estimate, you know whether you're talking about a fixed bid or a T&M arrangement.  Either way, you should give some serious analysis to the requirements of the project.  But if it's going to be a fixed bid arrangement, you don't give estimates, you only give bids, and you'd better be prepared to live or die by them.  It is amazing how tightly people will hold onto any estimate you give them and will judge your performance based on whether you met that estimate.  This happens even when the requirements change and you directly tell them that the estimate is no longer valid.  If this happens, I suggest you quickly give them a new estimate to hold onto so they forget the original.  Or so they really know how much their “little” change is going to cost in both time and money.

I have been unfairly judged in the past because I didn't know that I should give a new estimate when the project changed, but no new estimate was requested.  It can get really tense when your client is threatening to not pay, or when he does pay, and then proceeds to bad-mouth you.  Prevention is a better way, so give them an estimate even if they didn't ask for one.  (The one exception I can think of is when you're working in a staff augmentation role, but even then, time estimates are good, even when the cost is essentially fixed.)