1. Create a DNS record for subdomain and name it to something like downloads.byuu.org
2. Put a file there. The preferred naming scheme is to categorize it by product or product category, so something like downloads.byuu.org/emulators/higan.zip will do fine.
3. Start by putting the downloads in non-executable file formats first, e.g. use higan.zip instead of higan.exe. It's a no-brainer for a Windows user to launch the file from ZIP archive
4. Make links to downloads from your main website as you would usually do
5. Everything should be smooth now
6. Your downloads.byuu.org subdomain will slowly gain reputation
7. Once it has an established reputation, you will be able to put .exe files there. Gaining the reputation will take about several months. I would expect about 12 months to be on a safer side
8. Enjoy and be creative