The beauty of being a renter is that you typically don’t have to worry about major repairs. If you think the water heater is leaking in your apartment, call your landlord!
If it is just a small puddle of water, it might something simple that your landlord can handle themselves, like a valve repair. However, if the water heater is old, they might need to replace it.
Make sure to check the terms of your lease if your landlord gives you any pushback. This is something that they should take care of, but some leases stipulate that the tenant needs to pay for any repairs and then they can deduct what they have paid from their rent.