Inception can take many forms. For some projects, it's a chat at the coffee machine: "Have a look at putting our catalog of services on the Web." For bigger projects, it might be a full-fledged feasibility study that takes months.
During the inception phase, you work out the business case for the projectroughly how much it will cost and how much it will bring in. You will also need to get a sense of the project's scope. You may need to do some initial analysis to get a sense of the size of the project.
I don't tend to make a big deal of inception. Inception should be a few days' work to consider whether it is worth doing a few months' worth of deeper investigation during elaboration (see the next section). At this point, the project's sponsor agrees to no more than a serious look at the project.