How is individual consciousness connected to other people’s consciousness?

There's no individual Consciousness in the first place to get connected with some other consciousness. There's only Universal Consciousness which is indivisible and ever present. This, however, this question (purposely written like this to educate) appears to be divided in each individual Being, owing to our primordial ignorance.

Objection: Then, the way I think and know a thing should be in the same way as by everyone else as the division is only apparat and not real?

This objection appears to be legitimate and let's take a more familiar example to compare to extract a meaningful answer. The electrical supply is same qualitatively and quantitatively through a set of cables. But one electric bulb appears dim and another very bright and one light appears to be white, in another it appears to be blue, even though same electricity is passing through the cables at the same time: Why?

The reason lies not in electricity but in the bulb that's utilizing the the same electrical energy but there's a great deal of difference in the "wattage" and the color of the bulbs, the instrument that's using the same electrical energy.

Similarly, even though the spiritual energy of Consciousness is utilized by different “Minds" the entity that utilities the spiritual energy of consciousness are of varying capacities and potentials the real "thinking principle " not the Consciousness. It's the mind that needs Consciousness but consciousness that needs any help from any outside source to "know", just as you don't need a torch light to see the Sun which is self luminous.

But this 'mind' is conditioned by the experiences recorded in mind since several previous births with the aid of 'thrigunas' of nature's origin imbibed by the mind.

By this it will be clear that the mind though very useful for studying objective reality, it's a hindrance for 'knowing the thing in itself' ' — the thing in itself is always being the Consciousness; this can only be known by Subjective experience, not by objective proof.