In vi/vim, how do I append to a file instead of overwriting it?

From :h :w:

                                                :w_a :write_a E494
:[range]w[rite][!] [++opt] >>
                        Append the specified lines to the current file.

:[range]w[rite][!] [++opt] >> {file}
                        Append the specified lines to {file}.  '!' forces the
                        write even if file does not exist.

So, if you have selected the text using visual mode, just do :w >> /foo/samples (:'<,'> will be automatically prepended). If you miss out on a >, Vim will complain:

E494: Use w or w>>