Since you placed the word "business" in quotation marks, I have to ask; are you a business? Do you have the license(s) required to conduct business in your area? Do you have liability insurance? Do you have sold contracts, agreements and releases ready to go? Do you have a business plan and realistic pricing? Do you know who your target customer base is? If the answer to any of these is 'no' then, you shouldn't be looking for clients until you've taken care of that.
FAR too many people think that a facebook page is all that's required to run a business, and while you might (probably won't) make any money from it for the first while, you need to spend the money to have those things in place before you take in dime one. Your local municipality probably won't care how much you did or did not make, they'll take a guess at how much you could have made and levy a fine for operating an unlicensed business based on that. What happens when Mrs Smith's little boy trips over your light stand and cuts his head, requiring a trip to the emergency room and stitches? Do you really want to pay for that out of your own pocket?
All that is NOT to scare you off, rather to put you on the track of how to actually set up a business vice a "business". Once you've got all of those things done, then you need to advertise. Heavily. The market is saturated with weekend warriors, and if you want to make any money, you need to rise above them. You need a strong, cohesive portfolio, a professional website, and you need to reach out.
Rather than a business card (which, if you're lucky, might get used as a book mark instead of just being tossed in the rubbish) meet with the management and offer to shoot a couple of sessions with clients, and provide them with prints to display, provided you can also have your name & contact information and a rack of business cards there. Do the same for businesses. Print & distribute flyers, and don't be shy about passing out your card at every opportunity.
Thanks for the advice. I put business in quotes simply because I am still testing the waters, and don't really know where it is going to take me yet. I am actually doing all of my family shoots for free at the moment and intend to register my business with the city I live in beginning next year. I am doing everything for free right now and just getting started.
I would be happy if this was nothing more than a way to fund my hobby, and I'd be even more happy it I could keep it as informal as possible. My pricing is such that people don't have to feel like they are taking a huge risk, and they will know exactly what they are getting. But, if it takes off, then it takes off and I will cross that bridge accordingly. As far as insurance, I doubt I will ever make enough cash to warrant it.
I think that sometimes the people who are successful in the photography business look down on the newcomers who have no experience. I see it a lot. There are those who think that if a person has the attitude of "I'll do a few shoots a year and make some cash" that there is somehow something wrong with that. If someone wants to pay big bucks for an excellent photographer, they are out there in spades. If someone knows me through a friend and wants me to spend a couple hours with them for a reasonable price so they can get some Christmas cards together, I'm your guy.
There is no reason hobbyists can't do this on the side in an informal way to get experience, make a little side money, and have FUN. I fall into the "weekend warrior" group you mentioned. If weekend warriorism (a word?) is a big "no-no" here, my apologies. If I want negativity, I'd turn on the news.
(This isn't aimed at you tirediron, I very much appreciated your feedback. Things can get negative quickly when amateurs are involved sometimes...)