There are many ways in which one can discover the city, that is Delhi. You can take a tourist bus or a taxi or devise your own methods.
The basic intention should be to discover something new. Some innovative methods would be to take an auto rickshaw or devise a walk or take the metro, better if, it could be a bicycle ride. The idea here is to shun the known modes of transport in the city and to go those places you have never been. Try 'sadar' for example, 'old Delhi would be a good choice, or satellite townships (Gurgaon, Ghaziabad, Faridabad etc.).
There are two ways to approach this discovery process, the first is planned process and second the unplanned one.
The planned process would inevitably be based on (i) time and (ii) location (of the area you want to discover). Here how much time you are willing to devote is important. The time you want to devote would depend on the location you want to discover. So, you have to research on the area you want to discover and then plan you way around. Its a scientific approach.
The unplanned discovery method is just the opposite. It is time independent, but place specific. You can choose the area you want to discover, say Lutyen's Delhi and spend an whole day to locate the building in this area and their architecture.
In both cases, your desire and motivation plays an important role. Some like me are only a few years old in Delhi, some have just arrived and there are Dilliwallas. There is test to decide if you are ready : Ask yourself, are you bored of the city? If your answer is yes, then you are ready. And if your answer is no, take your time.
By the way, a good way to start would be 'Delhi: The Emperor's City by Shri Vijay Goel'. it has good pictures to motivate and a tapestry of facts to hold your attention.