How to convert a recursive function to use a stack?

Suppose that I have a tree to traverse using a Depth First Search, and that my algorithm for traversing it looks something like this:

algorithm search(NODE):
  doSomethingWith(NODE)
  for each node CHILD connected to NODE:
    search(CHILD)

Now in many languages there is a maximum depth to recursion, for example if the depth of recursion is over a certain limit, then the procedure will crash with a stack overflow.

How can this function be implemented without the recursion, and instead with a stack? In many cases, there are a lot of local variables; where can they be stored?