Which planet is this (if any)? I live in Ahmedabad, in India, with an exact location of about 27.2048° N, 77.4975° E. Currently (as of this writing), it is 20:52 EST. I noticed a red object in the sky.


(Forgive the crude imaging. I took this with my phone camera.)
Now, the brighter object is the moon, and the less shiny object is the red one I saw. I read somewhere that Mars would be visible right now, as it is closer to the Earth.
I also read that Mars and Jupiter appear red, with Jupiter slightly dimmer.
I wanted to know whether the object I just saw was indeed a planet. If so, which one (and how can I identify them)? Or is it just another star that I spotted?
Stellarium shows the Moon and Mars very close together in the sky tonight (Saturday, 3rd October 2020), so yes, it was probably Mars that you saw.
Moon and Mars on 2020/10/03 (Stellarium)
Stellarium is a great tool for identifying astronomical objects (and satellites), and is absolutely free.
Very rough rules of thumb for identifying planets by eye:

Very bright, white, and low in the sky (early morning or evening): probably Venus (but might be Jupiter).
Bright, white, and high up in the sky: probably Jupiter (unlikely to be Venus, which stays close to the Sun).
Bright and red: probably Mars.
Moderately bright and pinkish: probably Saturn.
Faint, white, and low in the sky (early morning or evening): might be Mercury.
If it scintillates (twinkles), then it's a star.

Jupiter and Venus are easily confused, since they can both appear to be bright and white. You really need to consider the time of day and the elevation (how high it is in the sky). Since Venus is closer to the Sun than the Earth, you are more likely to see it in the morning or evening (before sunrise or after sunset). Venus can climb quite high in the sky, but it will never be more than 45° in elevation.