A child process inherits most of its attributes, such as open files, from its parent. In UNIX, a child process is in fact created (using fork) as a copy of the parent. The child process can then overlay itself with a different program (using exec) as required.
Each process may create many child processes but will have at most one parent process; if a process does not have a parent this usually indicates that it was created directly by the kernel. The very first process, called init in UNIX, is started by the kernel at booting time and never terminates; other parentless processes may be launched to carry out various daemon tasks in userspace. Another way for a process to end up without a parent is if its parent dies, leaving an orphan process; but in this case it will shortly be adopted by init.