Explain me please how to download a file from a server using SSL (https://). I have not found an appropriate answer in the Internet.
Everybody says about TIdSSLIOHan
Download openssl-1.0.0d-i386-win32-rev2.zip , not openssl-1.0.0d-x64_86-win64-rev2.zip from http://indy.fulgan.com/SSL/
Read here too: https://forums.embarcadero.com/thread.jspa?threadID=15569
It is essential to get the correct DLLs as some are compiled with links to M$ Studio and therefore do not work in Delphi. Try https://indy.fulgan.com/SSL/ Latest versions are at the bottom of the page.
To use Indy's OpenSSL class, you need ssleay32.dll and libeay32.dll. That probably should have been apparent from the source of the exception in the Indy code you tried to execute.
The libraries are linked to from the Indy page mentioned in the question. If you're legally allowed to do so, you can distribute them with your application. Put them wherever DLLs go (usually your application directory).
TIdSSLIOHandlerSocketOpenSSL is an OpenSSL-specific descendant of the abstract TIdSSLIOHandlerSocket class. If you were using some other SSL library instead of OpenSSL, you'd use a different descendant class.