The basic meaning of the phrase "govern yourself accordingly" is to act in accordance with the demands of a document, such as sending money or contacting a lawyer. The phrase frequently appears in legal documents such as demand letters.
The phrase is often seen as a cliché because it appears so often. It is also seen as vague language unless the terms set in the document and the consequences for not meeting the terms are specifically laid out and a time frame is given. "Govern yourself accordingly" can also be taken to mean, "Do whatever you feel is best for the situation."