Baptisms are performed by a living person "on behalf of" a dead person. No one gets possessed or anything. 
 
Many people do report feeling a very close kinship, almost a presence, with the ancestors for whom they are being baptized.  
 
At the end of the day, there is no way to know whether or not the person has accepted the ordinance performed on their behalf.

This is from an article that President Hinckley wrote: 
 
"Through living proxies who stand in behalf of the dead, the same ordinances are available to those who have passed from mortality. In the spirit world these same individuals are then free to accept or reject those earthly ordinances performed for them, including baptism, marriage, and the sealing of family relationships. There's no compulsion in the work of the Lord, but there must be opportunity." 
 
President Gordon B. Hickley, Article "Why these Temples?" 
 
They are performed just as you would a normal baptism, just someone else is baptized for them "in their behalf."  
 
It is up to the person who has died, and now on the "other side," to have the chance to accept or reject that baptism that was performed "in their behalf." They aren't "forced" into the Church by that baptism or anything like that. They still have their free agency to accept the gospel.

In many Christian religions you are required to be a member here on earth to go to heaven but we believe that after death you have the chance to accept the gospel, which is where baptisms for the dead come in