From what I know of, Foodpanda is a great food delivery app/site. They deliver your orders quite fast as well, that's why they are used by lots of people. Since they also have an app version, it's quite easy to get acquainted with the mechanics. You only need to fill out your profile and save your favourite restaurants. This way, it's easier to order your favourite foods or dishes. You have the option to pay on delivery or pay via credit card. This app works in cities like Mumbai and Delhi.
Another great app/site to use in India is JustEat. This app doesn't have much of the restaurants as compared to Foodpanda, but it's very popular in cities. You can also pay via credit card or pay cash on delivery. But some users reported that the service of this app isn't as great as others. So that's one thing you'd have to consider before using it.
Lastly, is the undeniably very popular Zomato. This app offers reviews of different restaurants all around the world and including India. It's almost like a social media app just for foodies. The great thing about this app is that it's pretty diverse and has lots of members. So even towns and other cities apart from Mumbai and Delhi are included in this app.
So these are some of the apps any tourist or local in India can use for ordering food online. Apart of course from the online delivery services of famous fast food chains and restaurants.