Newspapers, online, and Apartment guides.
I searched all three and eventually found the apartment I'm in in an apartment guide.
Always ask what the pet policy is. The ad may say 'Dogs allowed', but a lot of apartments around here had size restrictions. (30 lb or less only) Quite a few had breed restrictions.
Not to discourage you, but apartment living with a pet is more expensive than on your own. There are pet deposits and monthly pet fees on top of the rent.
Start saving now! 
There is a college near by so there are always deals going on around May when all the college students go home for the summer and in the fall when they come back.
Good luck!
~Kimmy, Zam, Logan, Raptor, Nimrod, Mei, Jasper, Esme, & Lucy Inara
RIP Kia, Chipper, Morla, & June
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