Well, the most robust way would be to write a parser for the file types you want to detect and then just try – if there are no errors, it's obviously of the type you tried. This is an expensive approach, however, but it would ensure that you can successfully load the file as well since it will also check the rest of the file for semantic soundness.
A much less expensive variant would be to look for “magic” bytes – signatures at the start or known offsets of the file. For example, if a file starts with an ID3 tag you can be reasonably sure it's an MP3 file. If a file starts with RIFF??? WAVEfmt, then it's a WAV file. However, such detection cannot guarantee you that the file is really of that type – it could just be the signature and following that garbage.
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