Nope, no soul, no afterlife, no spiritual element. When we die, we're gone.
As for ghosts, hauntings and the like, I explain them much as I explain most supernatural/religious beliefs. People are good an seeing agency and patterns where none exist. We're masters of turning the fluttering of a tablecloth due to a puff of air from a cracked window into a poltergeist, the creaking of a settling house into a restless spirit. We've never found any actual evidence of ghosts, just wishful thinking and imaginative stories.
How do you explain ghosts or hauntings, or things like that?
I'm still yet to encounter one to explain...
What happens when you die?
You go back to the same way you were before you were born.
I am struck by the finality of death as I think about people I have known who have died. I believe that there is no soul, but there is immortality of sorts, in the form of information passed on in the form of DNA, in how the person's life affected others while he or she was alive, and in the knowledge a person leaves behind in forms accessible to others, Our chemicals also return to the cosmos, eventually, possibly, to be part of a series of cosmic events that leads to the creation of new stars, planets, and maybe even bits of life.
I do not think there is a "soul" that continues on after death. When our brains die, we are dead, for all intents and purposes. The person that existed exists no more. This is a sad proposition, and I understand why people want to believe otherwise.
As Strega mentioned earlier, our 'consciousness' is a product of our brain. One of the evolutionary traits of humans is that we have been able to continue learning for our whole lives, and learning at an extraordinary rate.
Every generation appears to be able to learn more than the last, building on the information of the previous generations. Now, in this age of communication, we have access to more and more information, all, quite literally, at our finger tips. Scientists can peer review theories in days now, compared to weeks or months previously; collaboration is so much easier now and giant strides are being made in technological development in all fields.
We are, every one of us, the result of everything that we have learned and experienced, no more, no less. If we live in a religious family and in a religious environment we will have been taught that we have a soul, that there is a god, that souls go to heaven (Valhalla?) or hell (Hades?) and that we have to do everything our religious leaders tell us to do, to ensure one and avoid the other, even if it is to the detriment of others (women, children, gays, ethnic minorities, other religions, etc.) It has always been so.
Think about everything you 'know' about souls. Who told you they existed? Who told them they existed? Why did they tell you they existed? All religion is an ancient method for control of the populace and the only hold they have on the individual is by the fact that your 'soul' is at risk if you do not do as you are told. It is, quite literally, the oldest trick in the book.
You are on here asking questions, continue to do so; learn about everything you can, use your obvious intelligence and curiosity to find the cold hard facts from the latest, verifiable, repeatable research. Do not accept simple answers like 'because the bible says so' because the bible has been saying the same thing since the earth was flat and the sun orbited the earth.
So the short version of the answer is: There is no soul, when you die your body deteriorates and rots just like any other carcass. If I die young, hopefully my organs will be used to help someone else have a better quality of life, the remainder will be cremated and provide food for the fishes. Hopefully that won't be for a few years yet, I have too much to do and too many to things to teach!