Question: Using only stdio.h, string.h and stdlib.h libraries how would I go about implementing this?

I'm quite new to programming so please bear with me!

Answer: 
1. Allocate a new `char` array of the same length as your string. Convince yourself that this is enough space. Don't forget the NUL.
2. Loop through the string, copying to the new string only those characters that are alphanumeric. You can't do this portably without also including `<ctype.h>` and using a function/macro from that header, unless you're going to enumerate all characters that you consider alphanumeric.
3. Again, don't forget the NUL.
Since this is homework, here is the verbal description:

Run a loop over the original string and use the functions `isalnum()` to determine if a character is alphanumeric. Maintain a second `char array` of reasonable size and every time you encounter an AlphaNum, insert it to that array. Once all AlphaNum characters have been copied to the second array, **NULL** terminate it and you have your string.

Note: `isalnum()` is defined in `ctype.h`, so if you aren't allowed to use that, you may have to define this function for yourself. That is another exercise of it's own.