There is a how and a when/where part. The how is fairly simple, as binary files do contain a header and the header is fairly easy to strip out and check. For windows files, you can check the article Executable-File Header Format. Similar formats are used for other binary types, so you can determine types you allow and those you do not.
NOTE: Linked article is for full querying of the file. There are cheap, down and dirty, shortcuts where you only examine a few bytes.
The when/where depends on how you are getting the files. If you are using a highly abstracted methodology (upload library), which is fairly normal, you may have to stream the entire file before you can start querying the bits. Whether it is streamed into memory or you have to save and delete depends on your coding and possibly even the library. If you control the streaming up, you have the ability to stream in the first bytes (header portion) and abort the process in mid stream.
MZ, odds are you've got an executable.