Sharing a house with other roommates definitely cuts costs a lot!
I have had the most success finding rentals like this on Facebook. Just type "<your city here> rentals and roommates" on Facebook and there will be groups for people looking for roommates and offering or seeking places to rent. Typically when you find someone offering a place for rent, you message them with a brief introduction about yourself and the lease term you are looking for (it usually helps to also mention things that would make you a preferable tenant, like being a non-smoker, quiet, being a student/stable full-time worker...etc).
You can either find someone to look for housing with in the group, or just find a room in a shared house and the landlord will fill in the other rooms. It's not always a bad thing to rent with strangers since I know several people who have destroyed friendships by living together and discovering their lifestyles drive each other crazy. The challenge in your case will be finding roommates in addition to a landlord who is okay with your pets.