Below are a few issues you may wish to address when drafting your pet policies. Provide tenants with a copy of your "pet rules" and have both of you sign it. You may want to consult with a qualified professional for assistance in drafting a suitable document.
Establish a reasonable number of pets a tenant is permitted within his or her unit, and state the types of pets allowed (dogs, cats, caged pets...). Keep in mind that many people have more than one pet, as pets like companionship, too, especially when their people are out! "Exotic" animals are usually not appropriate as pets.
If you live in a condominium complex, your contract may already set out conditions for pets in the units. One example is a condo that permits dogs and cats but disallows birds (some birds can be quite vocal and may disturb the neighbours).
Remember that the size of a pet doesn't necessarily dictate its behavior - for instance, many large dogs are well-behaved and quiet.
If you want the tenant to get permission from you prior to adopting another pet, be sure to state this in the agreement.
Tenants should keep pets within his or her unit. Pets should not be permitted to roam free, including when unattended on balconies, patios, decks, etc. Cats should be transported in carriers when moving through common areas, and dogs should be on a short leash.
Provide details if there are specific areas on the property which are available for exercising pets.
Specify where pet waste should be disposed (eg. is there a specific garbage can, and if so, where is it located?), and how (eg. double-bagged).
Excessive barking, meowing, or other pet-related noises can disturb other tenants and neighbours. Define what level of noise is unacceptable.
Likewise, pets should not be permitted to behave in an uncontrolled manner (harassing other tenants, relieving themselves in hallways, etc).
State the procedure if you have reason to believe there is an emergency situation involving the tenant's pet (fire, flood, abandonment, etc). For instance:
Tenants are responsible for any damages caused by their pets.
If your rental unit is located in an area where fleas or ticks are a concern, then you may wish to ask tenants to ensure pets are on a recognized flea preventive (or they could be responsible for the cost of treating the area).
Specify what happens if there is a complaint, or if the tenant is alleged to have violated a part of the pet policy agreement.
Your local landlord / tenant board for may be able to provide you with more information, specific to your area, about renting to people with pets.