Copying text out of an email uses your device's own text selection, so it works the way it does everywhere else on your phone or computer.
Android
Long-press the text you want. It highlights and a toolbar appears above it. Tap Copy. Drag the handles at either end of the highlight first if you want more or less than the word you pressed.

iPhone and iPad
Touch and hold a word until it highlights, then drag the blue handles to cover what you want and tap Copy in the menu that appears.
Windows, Mac and Linux
Click and drag across the text, then press Ctrl + C (⌘ + C on Mac). You can also right-click the selection and choose Copy.
Copying a Link Instead of Text
To copy where a link points rather than the words shown, long-press the link (right-click on desktop) and choose Copy link address. That gets you the URL without opening it, useful when you want to check where a link actually leads. See phishing links for why that's worth doing.
Once copied, the text is on your clipboard and can be pasted anywhere, a new email, a note, a message. To copy a sender's address rather than body text, see how to copy an email address.