First, you can find a file’s encoding like this:
$ file oldfilename.txt oldfilename.txt: ISO-8859 English text
Then, if you want to convert the file oldfilename.txt from ISO-8859 to UTF-8 and call the new UTF-8 file newfilename.txt you do like this:
$ iconv -f ISO-8859-1 -t UTF-8 -o newfilename.txt oldfilename.txt
Note that the file command says ISO-8859 and that you have to use ISO-8859-1 in the iconv command.
For a long list of available iconv encodings, use
$ iconv -l