How can I claim against my employer if I feel that I have been dismissed unfairly?

In order to claim unfair dismissal you will need to have the necessary qualifying period of service.  You should fill in a claim form ET1, available at www.employmenttribunals.gov.uk . This normally needs to arrive at the Employment Tribunal within 3 months after the dismissal unless the tribunal accepts that there were special circumstances that prevented the claim being presented in time. The time limit is applied very strictly by tribunals.