How do I make an object follow a path that can be switched seamlessly with another path?

The title may seem confusing. Here's what I am trying to achieve.
I am trying to make a minecart follow a rail. There are multiple switches during its run that change the rail's course from one path to another.
Firstly, how can I make an object move following a path.
Secondly, how can I make the object switch paths while running through script?