Are you located in a retail area or ? Is this going to be a full time shop or open certain hours?
The VERY best advertising you can have is happy satisfied customers. It will take a year, give or take, for business to become steady, or even enough to pay the utilities without covering other costs.
Use your first few months to quilt everything you can find - pillows, wall hangings, cheater tops, charity quilts, any and everything - and in a variety of styles AND take lots of pictures. Hang / display lots of finished products.
Everyone coming in will want to see your work.
Go to Guilds, Clubs, enter Quilt Shows - everything to get your name out there. Become friends with your LQS and Chain fabric stores (More than just leaving cards). Grow a thick skin as there are still many people who don't 'get' LAQing...
The quality of work, your rates, the turnaround time, pets or not in the area/shop, hours of operation will all get you business. BUT it will also take a bit for all of that to come together.
You might consider a referral program or frequent quilt program for your customers for the first year (or longer even) - maybe every 5th person referred qets them 10-20% discount on quilting (not thread, batting, etc.) or every 5th quilt they get 10% off.
Be flexible for the first few years - find what works for you in your area, for your customer base. Know what you're willing to work during the holiday season - are 12 hour days 6 days a week between Thanksgiving and Christmas acceptable to you to crank out the volume?
If you've gotten far enough to be ready to open - you're in it for the long haul!
Hang tough, be creative and enjoy the ride!