How to measure Johnson Noise precisely experimentally?
"but practically I am facing some problems with circuitry."

Oh yes, I'll bet you are. You've stated in comment that you "don't have much resources", and this will probably be an issue.

Measuring Johnson noise is quite straightforward: You put a high-gain op-amp across a resistor and measure the output. Then you short the input and look at the output again. The difference is due to the noise in the resistor. Of course, the devil (or God, depending on your source) is in the details.

First, you need a very low-noise op amp - one with a specified noise input well below the predicted resistor noise. These are actually pretty cheap these days, but you can't use just any op amp you have lying around. You most definitely can't use a 741, an LM2900, or pretty much any general purpose (really cheap) op-amp. You CANNOT use a wireless breadboard, even if you keep the leads much shorter than most breadboarders do. And you need to put the circuit inside a Faraday Cage: the ether is filled with all sorts of stray EM fields, particularly around 50 or 60 Hz. None of this is horribly expensive, especially if you can find a source of double-sided pc board scraps for your enclosure. You can find very cheap sources for small pc board prototypes for building your circuit, and there is free software which will allow you to produce the etching masks, but you'll need to do your homework.

For inspiration, I suggest you study the "What's All This ..." articles written by the late great Bob Pease.