If you want to copy a range of text, drag the blue circular bars at each end of the highlighted word to select the text you want and then tap Copy in the pop-up menu.
In some apps the pop-up menu offers Select/Select All options. In this case, select one of these options and then select Copy.
Now, when the text is copied, you can then paste it.
How to copy images:
Simply tap and hold your finger on an image and choose Copy.
How to paste text and images on iPhone:
If you want to paste the copies text or image to another app, open it, tap the place where you want to paste the text or image and hold your finger until the magnifying glass appears, then remove your finger and tap Paste in the pop up menu.