Delhi is a large sprawling city. If you would like to use road transport to go from place to place, then you can use call taxis or private car rentals.  

Call Taxis are a convenient and comfortable way to get around the city. There are professional taxi companies operating in the city. You can phone and pre-order a taxi. Some also have websites where you can book online.

There are additional service fees involved in case you book a cab at night time (11pm-5am). 

Call taxis operate by the meter. Most taxi drivers do not speak English; however if you are going to a popular landmark or a well known hotel, they can take you quite easily.  To avoid misunderstandings, make sure you know a popular landmark near the place you wish to visit. You should also familarise yourself with a map of the city with the desired destination distinctly marked. Call taxis are not always available when you want them; especially in peak traffic hours. So it is better to book at least 2-3 hours in advance.  

As an alternative to call taxis, you could also pre-arrange private car rentals. All hotels - from the smallest B&B to the big luxury hotels - can usually arrange private cars. Usually, the luxury hotels provide more expensive car rentals, with English-speaking drivers, bottled water, cold towels etc. Smaller hotels offer more inexpensive rentals. Please check if drivers speak English.

Apart from hotels, there are also several private car rental companies in the city. Travel agents and tour operators in the city can arrange car rentals for exploring Delhi as well as for longer trips to cities in and around Delhi.

You could possibly visit the Tripadvisor Delhi Forum for reviews and recommendations for car rental companies. The Forum also has useful information on sightseeing, shopping and dining in Delhi.