1. They told their twenty-year-old son that it was time he found a job and began to support himself. It was time for him to stand on his own two feet.
2. 1 was so glad to hear that Pete and Gloria got a house of their own and that they no longer have to live with her parents. They are finally standing on their own two feet.

The expression suggests that when a person uses his own two feet, he is not relying on others for support. The expression always calls for two feet even when the subject is plural (opt.2) and four feet would be more logical.