When you select a single word, you'll see it highlighted in light blue. At either end of the word, you'll also see a blue line with a dot on the end of it. Those boundaries signify what you're going to copy.
To can drag the boundaries to select more words to copy. To do so, tap and drag either of the blue lines in the direction you want to copy (though you can't drag the left boundary across the right one and vice versa).
When you've got the selection you want, tap copy.