One way to select a word or a couple sentences on an iPhone is to tap once to place your cursor in a text field, then tap again to choose the Select or Select All option from the popup bubble, then perhaps tap a third time on one of the selection markers if you need to expand the selection.
A faster way is to simply double-tap the word you want to select. If you need to expand the selection to more than a single word, tap-and-hold on the second tap and begin dragging left, right, up, or down from the word you selected. iPhone OS will do the right thing and increase your selection in any direction, keeping the original word you double-tapped as either the beginning or end of the selection.