the first contact to you as a trainer is often an email. It is nothing but a starting point for a conversation. In your subsequent phone call you can ask about how the person heard about you. Most personal training is word-of-mouth.
What I often do it to check what I can find out about the person through available online searches such as Facebook.
If you are asked to go to a person’s home, you should first meet in a public space as Natalie suggest. If it is a serious offer,the person should not feel offended by your precautions.