Learn Portuguese (Portugal): Por favor, senhora!

It is the exact equivalent of "please" in English, but literally it translates to "by favor" or "for a favor". Por means "by" or "for", and favor means "favor".

Why is it just senhora and not a senhora?

When you are directly calling out to someone to get their attention (like saying "Madam!"), you leave out the word a (the). You only include the a when using a senhora to mean the formal "you" in a sentence, such as "How are you?" (Como está a senhora?).

How do I pronounce the nh in senhora?

The nh sound in Portuguese is just like the "ny" sound in the English word "canyon" or the "ni" in "onion".

Can I use this exact same structure to get a man's attention?

Absolutely. You would just swap senhora for senhor, making it Por favor, senhor! ("Please, sir!").