IDM (Internet download manager) API using C#?

You should

1) download IDMCOMAPI.zip to your disk

2) extract the IDManTypeInfo.tlb type library from this zip file, somewhere on your disk

3) run The Type Library Importer tool like this:

[C:\Temp]"c:\Program Files\Microsoft SDKs\Windows\\v7.1\Bin\TlbImp.exe" IDManTypeInfo.tlb
Microsoft (R) .NET Framework Type Library to Assembly Converter 3.5.30729.1
Copyright (C) Microsoft Corporation.  All rights reserved.

Type library imported to IDManLib.dll

This will create an IDManLib.dll

4) Now you can reference IDManLib.dll in your project. I have not tested it, but I also suppose you want to ensure your program is compiled with the proper bitness (it depends how the IDM COM Server works). So, I suggest you compile as X86 (not anyCpu, not X64).

The API seems to be a COM object - did you try looking for it in the Add reference dialog? COM objects are registered globally, and judging by that page it should be there if you've run "IDM" on your computer.