As with every product development, software development has its stages:

Analysis,
Design,
Implementation and Unit Testing,
Integration
Verification.

The various process like

Waterfall,
RUP (Rational Unified Process),
Agile and
Lean 

tells us various way of working on these stages. The best way of working is decided by the team, usually by the ones who has authority and chosen from one of the above process according to the current situation of the project (yes situation of the project can change the process!)

While there are debates that one of the process fits or combination of process fits the project, it is generally depend on the experience of the team members on these process. While it is advised to have at least one member who directs the team on these process, general case is not so. Hence generally according to the experience of the most experienced members, the processes are adapted and they will be generally the combination of the process from the above ones and picked as the best by the project authorities - Managers, Architects, Leads etc.

So what process does OO follow? The answer is there in above paragraph. The OO is a paradigm, a thought process to do Analysis and Design but not the process which guides the project. Hence in all the process listed above, OO can be applied and especially in the stages of Analysis and Design. The implementation and unit testing depends on the implementation language and testing framework and the chosen process.. Integration and Verification depends on the process and the tools used for them.

Before going in to discuss what is OOAD, we have to understand how we 'think' usually.

While there could be many thinking that exists before OO, it is very common to think in procedural oriented way as that was the latest development before OO has come to party.

So what is that thinking and what is the procedural way, a short recap:

As the software development happens only when there is a requirement, let us take some requirement.

Let us take the example of coffee maker.