(Note: If you're willing to read a lot about this, this https://uusyrityskeskus.fi/wp-content/uploads/2021/02/Perustamisopas_2021_EN.pdf is a good manual for that (it's a very large PDF file).) The following is an extremely simple guide on how to found a company in Finland fast.
What's the type of the company (Toiminimi (sole trader/private trader/private entrepreneur, very simple, tied to yourself only) or Osakeyhtiö (OY) (Private Company, LTD) or other. I went with Toiminimi. You can convert it later to OY if wanted. Toiminimi is cheaper to found and easier to manage.
Either apply for the state-funded Starttiraha (Startup grant), which means you aren't allowed to found your company or start your business (even publish the website or do any marketing) until you've been accepted for the grant. This is the route I went, but it takes some effort to fill in the paperwork. You can use the same address below to learn about this.
Or just ignore everything and register the company and get the company's Y-tunnus (business ID) fast and you're ready to go. You can found the company and also register it in the Trade Register (Kaupparekisteri) to protect the name of it in here: https://www.suomi.fi/company/business-start-up-wizard - Founding a Toiminimi, like I did, costs 60 euros - it used to be free if you don't want to protect your company's name in the Trade Register, but it may not be the case anymore.
In the link above:
Unemployment fund - I went for this, seemed a good choice, but you need to pay quite a lot of YEL insurance to do this.
Estimate your annual turnover - I estimated under EUR 15,000 at first, easy to change it later to larger if your income becomes higher.
VAT prepayment register - I registered, I think it's somewhat mandatory.
That's about it, but I will edit this page later to add more info about the process.