There are different ways to do this.

One way is to have another array to remember which word has already been used (logically this is a bit mask), so you would not pick a used word twice (assume this is one of your requirement).

1. For the first word, you just generate a random number within the range of array index, and pick the word at that index. Also mark it as used.
2. Start from the second word, you generate a random number r first, if the word at index r is not used, pick it, and mark as used; if it is already used, check whether r + 1 is used, this goes on and on, until you find an unused one. Imaging the array as a ring, when you reach the end, go back to the beginning.