How can I get a Mandarin teacher while living in a small town without Chinese schools/institutions?
There are a few options: 


Finding an online tandem partner who speaks Chinese and is interested in learning a language that you can teach (your native language or another language in which you have a near-native proficiency). Mosalingua lists a few sites where you can find a tandem partner; there are several other ones, e.g. Polyglot club. See also How I found Chinese speaking friends online on ChineseForums.com. 
Finding a paid tutor or teacher. The classifieds section on ChineseForums.com might be helpful here. Some of the sites that help you connect with tandem partners can also help you find paid tutors or teachers. The actual teaching may work through Skype lessons or through video conferencing functionality built into the site.