In the new Justice League movie, we see that:

Superman is revived by being placed in a Kryptonian Regeneration Matrix.

It is pretty understandable that this can be explained to the public, as one such event has occurred in Batman v Superman: Dawn of Justice. This is pretty easily explainable because he is not a human and many things are still unknown about him.

Having said so,

With the death of Superman, Clark Kent was also dead and we see a detailed funeral service. When Superman came back, how do they explain the return of Clark Kent, who is assumed to be just another human being, working in the Daily Planet?

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    They just say that it was Lois Lane's dream and Clark was in the shower all the time. No wait, that was Dallas. – Chenmunka Nov 22 '17 at 8:51
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    Trouble with the "fake burial" theory is that the funeral held in Smallville in BvS was open-casket and everyone who attended saw Clark's corpse... – Dave Nov 22 '17 at 9:00
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    Then he was cremated, and he emerged with severe burn marks. No wait, that was My Hero. – Mr Lister Nov 22 '17 at 9:07
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    Does "I am Mark Kent, Clark's evil twin, and I have not come in peace !" make a valid reason? – Varun Nair Nov 22 '17 at 11:10
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    Maybe he was injured on a trip to the mountains and got lost. The body in the casket was his long lost twin (the two were separated when they were adopted), who happened to die around the same time. They thought the twin was Clark, so they didn't realize he was missing. Once he healed up and hiked back to civilization they realized the mixup and he was brought "back to life", including his old job. – Dan Smolinske Nov 22 '17 at 16:30