The trouble is that the text has a different encoding from what you're using on the page you're displaying it on.
What you want to do is find out what encoding the data is (for instance by looking at what encoding the page you take the text from is using) and converting it to the encoding you're using yourself.
For doing the actual conversion, you can use iconv (for the general case), utf8_decode (UTF8 -> ISO-8859-1), utf8_encode (ISO-8859-1 -> UTF8) or mb_convert_encoding.
To help you find out what the encoding of the source page is, you could for instance put the website through the w3c Validator which automatically detects encoding.
If want an automatic way to determine encoding, you'll have to look at the HTML itself. The ways you can determine the selected charset can be fonud in the HTML 4 specification.
In addition, it's worth having a look at The Absolute Minimum Every Software Developer Absolutely, Positively Must Know About Unicode and Character Sets (No Excuses!) for a bit more information on encoding.