To be sure I choose a reliable SEO, what questions could I ask to feel more confident it is the right one?

If I ask "how or what" then obviously they keep it vague (which i understand, nobody wants to actually TELL the techniques).

Anyone?

Thanks!!

Ask them whether they use white-hat methods or black-hat methods. If answer is yes get a list of methods they use.
Do yourself some research for the methods to verify them white-hat.

Good question, but I doubt that anyone who uses black hat would be willing to admit it. I suggest that you ask them to verify that they are currently on the first page of Google for their business. They should be ranking for anything that includes SEO... like the name of your their city of business and SEO. I would avoid any SEO would could not rank this search.

Think of it this way, if they can't get themselves on the first page how will they ever get your website there!

I think we should know that Do they require that I make changes to my website other then on page optimization?

True, true! Companies doing Black hat techniques will never say it openly. How bout like this - ask them if they guarantee #1 listing - if they do, more likely they are into black hat seo.