How much is your stuff worth to you? Could you replace it if it was stolen or destroyed if your home was lost due to a fire?
When you rent, your landlord's insurance protects the landlord's property; it doesn't protect yours. All your clothing, electronics, kitchen equipment: unless you protect it yourself, you're unprotected.
Renters insurance protects you in multiple ways. It provides coverage for loss of use, meaning if the property is damaged and uninhabitable, it will pay for you to stay somewhere until you find a new home. Your personal property is covered if it is stolen. And you are covered for personal liability, in case someone is injured in your apartment (if, for example, a bookcase falls on a cleaning person).
All policies have a deductible. If you have a $500 deductible and the amount of loss is $400, you don't receive any reimbursement. You will pay more for a lower deductible, so you need to decide if the risk is worth the extra expense. You also need to select the amount of personal property coverage by estimated how much all your clothing and household goods are worth. Additionally, you need to decide if you want replacement coverage. Normally items are covered for their current value. A TV you bought a year ago isn't worth what you originally paid. If you want enough insurance to be able to buy a new TV, you would want to insure its replacement value rather than the current value.
If you own very valuable property-- a lot of jewelry, art, or expensive photography equipment-- this will most likely not be covered by a basic policy. You will need to purchase a "rider" or "floater" to get more coverage. You may be required an appraisal to confirm the property is worth as much as you state. If you work at home, you should discuss with an agent whether you need a separate business insurance policy.
If something happens and you need to file a claim, contact our company, either directly or through your agent. They will collect the necessary information and make arrangements to send an adjuster to review the property, if necessary. If all goes smoothly, you'll have your reimbursement within a month.