Month-to-Month vs. Lease
Generally, the agreement will be a month-to month rental agreement or a Lease. A month-to-month agreement is just that, the tenant or the landlord can simply give notice (as specified in the agreement) and move. Whereas a lease is a fixed term agreement that generally covers 6 months or a year of time. In a lease agreement if the tenant must move (i.e. relocating for a new job) they are still liable for the rent on that unit for the term of the agreement.
The agreement will state the acceptable forms of rental payment, when the payment is late, the penalties associated with a late payment and the delivery method of payment. Read and understand exactly how to comply with the agreement before signing it.
Repairs and Alterations
If the agreement has a section dealing with repairs and alterations, potential renters should read it and ask questions if they don't understand it. Under California law, the renter is required to return the rental unit to the property owner in the same condition they received it, allowing for ordinary wear and tear. If unauthorized alterations are made to the to the rental unit (i.e. painting , hanging wallpaper, etc.), the tenant may find that most or all of their security deposit may be used to return the unit to its previous condition...or worse they could be required to pay for damages beyond the deposit.
Addenda to the Agreement
A potential renter should read all addenda to the agreement and understand them. Some addendums are required by law; others are used by the owner or their agent to maintain the property. In multi-unit buildings it's not unusual for the agreement to have house rules that govern things like parking, quite hours, pool rules, pet policies, illegal activity, proper cleaning, etc. Generally these rules are designed to minimize conflict between residents living in close proximity to their neighbors.
Reading and understanding the rental agreement will avoid conflicts and have greater enjoyment of a rental home.