To make an unfair dismissal claim, first, ensure you meet the eligibility criteria, which typically requires you to have been employed for at least two years. Start by gathering evidence of your dismissal, such as emails or witness statements. Next, submit a claim to an employment tribunal, following the official procedure outlined on the gov.uk website. You'll also need to attend an initial hearing where both parties can present their case. It’s advisable to consult a solicitor specialised in employment law for guidance tailored to your situation.