The general strategy would be to get the previous text, append the new
String to the old text, then add the text back to the TextView. It may be a little more complicated because you probably want to add a line break, and maybe other conditions (like a fixed number of lines to display, scrolling, or something.
An alternative to the TextView which may better match your goals might be to use a
ListView. The ListView can be bound to an
ArrayAdapter. Whenever you get a String you would add it to the ArrayAdapter, which would cause the ListView to expand to accommodate the new text. It makes it easier to control the values which get displayed (the number of lines, formatting, etc...)