Numerous companies operate at Helsinki Airport, and they all have separate hiring processes. Please contact directly the company you're interested in to inquire about job opportunities.
Apart from the airport operator Finavia, operating companies include airlines and their ground handling companies, security control, restaurants and cafés, shops, lounges, cleaning services, car rental companies and money exchanges. Restaurant and shops also partially rely on temporary agency work, so agencies like Barona and Staffpoint are also worth checking out.
You'll find up to date information on services and companies of the airport at Finavia website.