Ok, so I can use dumpbin.exe /exports library.dll to find all methods in the dll.
...but how do I find out which arguments to pass into them? Without a header file
For the usual C-style exports (e.g., Windows API DLLs): You can't. This information is not stored in the DLL and is inevitably lost after compilation (unless you have the headers or debuging symbols).
C++ exports, on the other hand, store their signature as part of the mangled function name and you can view them using Dependency Walker or similar tools, or demangle them manually using the UNDNAME tool or DUMPBIN's /SYMBOLS option.