What is the meaning of "get across (+ to)" ?
How can we get our message across to the public effectively?

Question

Answer

Well, on one level it simply means 'to communicate'.

'How can we communicate our message to the public effectively?'

But as Alena said it also means 'communicate in a way which is understood' AND also 'communicate in a way which is convincing and believable'.

So you could say:

"How can we communicate with the public so that they understand our message and believe it?"

Answer

It means 'make someone understand'. "How can we make the public understand our message?"