Always analyze the type of insurance you are purchasing. Make sure it is the exact type of coverage you want with a deductible that you can afford.
Store all of your insurance documents and receipts in a safe deposit box or with an attorney.
Try to periodically take up to date pictures of your property and keep them with your insurance information.
In the event of an accident, keep a clear log of your interactions with adjusters and agents concerning this matter. This includes any conversations whether in person or on the phone.
Purchasing renter's insurance is always important. A popular misconception is that your property is going to be covered under your landlord's property or homeowners insurance policies. This is not always the case and it's better to have your valuables insured just in case.