You will be notified, usually by mail, of what they decide. If you receive notice that your claim has been denied or that there is no coverage, you can try to work your way up the system until you get to someone who will treat your claim seriously. Some insurers are notorious for having a policy of denying claims on the first attempt, on the assumption that most people will be discouraged or intimidated from pursuing it. If you have a claim you feel was unfairly denied, an attorney can help you negotiate with the insurer. Sometimes, it only takes a letter from an attorney to make an insurer change its mind.
Some insurance policies provide for mediation or arbitration of coverage disputes.
If your policy contains such a provision, you will present your side of the case to a neutral person who will decide whether or not you have coverage. If you receive notice that your claim is accepted and that you are entitled to coverage, a number of things can happen. In health insurance and auto liability insurance, it is typical for the insurer to pay the health care provider or the person you hit, and inform you that they have done so. In life insurance policies, it is typical in uncontroversial cases for the insurer to pay the benefit by return check, although they will require proof of death. In homeowner's or renter's policy claims, the insurer will want proof of what was lost, and in some cases require that you replace what is lost and then seek reimbursement.