Go here and read the Select Words or Paragraphs: and Copy and paste text sections for how things generally work in an editable text field.
http://help.apple.com/pages/ipad/1.6.1/#tan7248aac9
Not mentioned is the ability to tap and hold in the text until a magnifying glass appears. This allows you more precision in placing a cursor. When you release you'll get a Select and Select All option. The first selects the nearest word, which you can then expand using the drag handles (blue dots).
Open the Notes app, or any other text editing app you have hand, and play around with how things work. You'll get the hand of it more quickly than you think.
Other apps may or may not support text selection and copy. If it does work, the same gestures usually apply, but may have different outcomes; such as only being able to select entire lines or paragraphs. Safari is notorious for this, mostly because of the many different ways to display text on a website.
Go to a few sites in Safari and tap tap around using the same gestures, and see how they work.
One tip. If you can't select a picture, try selecting some text near it then dragging the selection handles to include the picture. On the pasting side, pictures will only paste into apps that support the feature. Not all, even the ones that can import picture, will do this.
Good luck.