Don't be in a rush. That is one of the things you'll hear several times, no doubt. In my lodge, most of the fellas visited for months before getting a petition. And you would be wise to wait until one is offered rather than asking for one, in my opinion - or at least, do not open the conversation with that.
Keep in mind that Freemasons aren't permitted to recruit - which runs contrary to the public perception that you must be invited to the lodge and to become a member.
Browse for the lodge's website, find out when they meet. Go to the lodge. Dress in a suit if in doubt about attire. Meet the men there. Shake hands. Expect to repeat this every time they have a meeting for several months.
Personally speaking, if someone showed up and requested a petition straight out I'd give them one, but sign it, no. Neither would any of the other men at my lodge. Maybe some lodges in different states are different - but your best bet is to see this as a process where you are building friendships first, brothers second.
Most of the men at my lodge spent months attending the meal before our lodge meetings before getting their petition signed. That is normal. The men who sign for you are putting their honor on the line for you, and one day you may do so for others. You yourself will want to know the man you are signing for, just as they will.
Whats more, there will have to be a vote on your petition once you get to that stage. An investigative committee will be assigned and their findings presented to the lodge prior to the vote. Depending on the state, one, or a very small number of negative votes is all it takes to end your candidacy. Better by a long, long way for every man who will be voting to know you, personally, prior to the vote. And I don't mean being introduced, I mean knowing you - what you are about, getting a sense of the sort of man you are. Otherwise they are voting on a nameless, faceless person to them and anything in the investigative committee report that raises their eyebrow will guide their vote entirely.
Look at it as a six month or so process from the time you visit the lodge till the time you are initiated. If it happens faster than that, great. But set your time frame realistically. This is not an organization you should hope to show up, get a petition, get it signed, and get initiated all within a couple of weeks or the like.
Focus on learning the names of the men at the lodge. It isn't one interview. Its many.
Good luck!