If you ever have to make a claim, the first thing to do is to call them and let them know exactly what has happened. You should then ask them to send you out the appropriate claim form. The form will probably ask you to provide estimated costs for repairs / replacements. If this is not always possible at this stage, you should complete as much of the form as you can and include a note to say you will supply estimated costs when they become available.
It may also be necessary to hang onto your damaged items as they are evidence that you are making an honest claim. If it is not possible to store the items in the house such as flood damaged items, you may want to store them in a shed or garage. Also, you should look out the receipts etc for each item you want to claim for.
When the insurance company receive your claim, they will either just pay it out, they may send a claims assessor to clear up any complications and to inspect any damage, or they may send out a loss adjuster who will be able to advise you on specialist areas such as how to get repairs done and where to find replacement parts.