Anna, most dance studios should be very accomodating to a person wanting to take lessons on their own without a regular dance partner. You could start by looking at the dance studio directory on this website or in your local yellow pages. Check some of the different studios around town, and see what they offer.
You'll find there are two main groupings of dance studios: Independent studios, and franchises (like Arthur Murray and Fred Astaire). Some people have problems with the latter group, so you have to be careful. The link below has a site which describes things to look for in a studio, and the pros and cons of going with either an independent or franchise. My biggest piece of advise on that front would be to avoid any studio which tries to sell you a huge package of lessons within your first few visits to the studio.
http://www.oldnslo.com/dance/index.htm
As for instruction, most places offer lessons in the form of 1. private one-on-one sessions with a professional, 2. group classes, 3. and practice parties. You really want to take advantage of all three in order to maximize your chances of getting better. Most places should offer different levels of group classes so that you don't feel overwhelmed in a group of experienced students. The classes and parties also give you a chance to practice with different partners and experience different leads. Typically, there are more women than men in groups, so you may have to wait your turn as the men are rotated.
I think what you're doing, starting out on your own without a regular partner is by far the BEST way to learn in the beginning. Couples that only take privates together or do the occasional group/party progress much slower and get discouraged more easily. One-on-One instruction with a pro will give an idea of how everything should "feel".
Best wishes as you begin your dancing. I think you'll find that you meet a lot of wonderful people doing this hobby. It changed my life, and I'd recommend it to anyone.