The best way for your pet (or the one you've found) to get a home is for you to find it for them. It's healthier, less stressful and more certain than anything else.
Best Friends has a wonderful pdf booklet on line you can download.
Run ads in the local newspapers, with pictures if possible.
In addition to ads, flyers are a wonderful way to advertise your pet. Include a picture and lots of details, and put flyers up at your work, around your neighborhood, and any place else you can think of.
Please do not offer animals "free to a good home." This will attract "bunchers" who take these animals and resell them to research labs. Keep in mind that people who aren't willing to pay even a small fee for an animal probably won't be willing to pay vet bills when it gets sick or have it neutered. Ask for a small donation, $20 is reasonable. If you don't feel right about accepting the money, donate it to your favorite charity.