Let's get one thing straight right off. What it ISN'T is Satanic or of the Devil, no matter what you may have been told by those who want you to believe thusly for their own ends. The Devil is a strictly Christian construct. I don't know of a single Pagan of any flavor, myself included, who "worships" Satan. In fact, if you call most Pagans "Satanists" they will either just roll their eyes, or laugh in your face at your ignorance and bigotry. "Satanists" are perverting Christianity for their own ends, and few self-respecting true Pagans will associate much with such people.
Then what IS a "solitary eclectic non-denominational pagan"? It's not too difficult. Let's take it one word at a time.
Solitary means alone, by one's self, of course. I do my spiritual practice alone rather than as part of a group. I have always felt that one's spiritual path was a personal and private matter anyway. My relationship with Spirit is between me and it anyway -- there's no requirement that anyone else be involved.
My solitude is partly by choice, partly by circumstance. I don't have an overwhelming need to belong to a group, and I refuse to join a group that isn't the RIGHT group for me. And I'm picky. I also REALLY don't like large crowds of people, so I don't seek out the various "gatherings" that occur where I could participate in group ritual. I have participated in the occasional cyber-ritual, which is an interesting hybrid of solitary and group work, but don't make a regular practice of it. The one true group ritual I ever participated in was a dedication ceremony with my six best woman friends (who are scattered all around the country), the only time we were ever able to all get together in person for a long weekend a few years back. It was wonderful, but that's because it was with the right people. Without that caring and bonding, I'd just as soon it be me and Spirit. We get along just fine with just the two of us.
Not bound to or by a single tradition, but borrowing meaningful and useful practices from wherever they may be found. In my case, I suppose that's a mixture containing quite a few ideas that seem to appear in many pagan traditions at once; some basic Wiccan, shamanistic, and Druidic practices; a hefty dose of Asatru-based honor, leavened and tempered with a dash of Zen Buddhism. That still doesn't describe it very well. You'd just have to hang around with me for a few months to start figuring it out.
See Non-Denominational as well.
I'm not an Official Card-Carrying Member of any particular brand of paganism -- not Wicca or Santeria or Asatru or Shamanism or The Church of the Grand Pooh-Bah or anything else. My own practices may show occasional similarities to any or all of the above at times, but I don't follow any specific doctrine. Not being currently part of a formally organized group, and never having been formally initiated into any Officially Or Otherwise Recognized Group, I'm non-denominational. It's somewhat like the Christians that just call themselves "Christian," without specifying or belonging to the Baptist or Methodist or Episcopalian or Catholic Church -- but only somewhat.
Strictly speaking, "pagan" refers to one who is not Christian, Jewish, or Muslim. I won't bore you with the etymology of the word "pagan" -- there are other sites out there on the Web where you can find that little tidbit of data.
Pagans can be monotheistic or polytheistic -- my own beliefs are rather mixed. I regard Deity as an "entity" (for lack of a better word) that transcends just about anything we can think of, including gender. Call it "Spirit" if you prefer. By whatever name you know it, it's something that's usually too big and grand and overwhelming for us to process and accept, so we filter that concept down to something we can wrap our perceptions around. Our filtering produces that which we call "gods" and "goddesses" -- entities with qualities and attributes that we can relate to and understand. If you're into anthropology or psychology, think of them archetypes if you like.
I recognize the male AND the female qualities of Spirit. In fact, as my own counter-reaction to the overwhelmingly masculine presence of Spirit in our culture, I tend to focus, not exclusively, on the female aspect. I'm more comfortable, for whatever reason, working with female aspects most of the time.
The Goddesses with whom I have a particular relationship are Northern European deities. The two that I've worked with most extensively are the Celtic goddess Brigit (known by many other names) and the Scandinavian minor (not to me!) goddess Skadi. Both ladies are strong, talented, and independent women, and have given me a lot of their strength to support me over the years. Brigit chose me first and became my first Matron Goddess, and pretty well set me into my current path. Skadi came into the picture more recently (at that one group ritual I mentioned above). Working with her has been, ah, interesting. She is a firm believer in speaking truth, to oneself and others, and since beginning to work with her I've found myself speaking my true mind a LOT more (not always comfortably!!).
Practice magic? The only magic I know how to practice is "The Goddess helps those who help themselves." If you want something done, be prepared to do it for yourself. On the other hand, I do perform rituals, even the occasional spell if you want to call it that. For example, I've been known to light a candle and meditatively focus on a goal, which some folks might consider practicing magic. However, lighting that candle and meditating never does the trick alone, because there has to be action on my part as well. The focus that little ritual gives me, though, always seems to help.
I suppose it depends on your definition of "practicing magic".
There's also the fact that everything is interconnected, and trying to force a change in one thing can have very unexpected and unintended consequences. I don't want the responsibility when something goes badly awry because of my meddling in things I don't understand.
To me, paganism is all about personal responsibility for my own actions and behaviors. There's a law known under many names on many different paths, but the Wiccans phrase it "An' it harm none, do as thou wilt." It seems like a very simple eight words, but start thinking about it and it gets tough. How do you define "harm," for starters? Then you discover that no matter WHAT you do, you WILL harm someone or something. Then it becomes a matter of choosing which and what kind of harm you will do and hopefully it's the least harm possible.
If this still gives you trouble, ponder the difference between ethics and morals. In my experience, Pagans worry about ethics and don't get too worked up about morals; fundamentalists of whatever flavor worry about morals and leave ethics high and dry too often. I ponder ethics a lot; the morals just don't bother me much.
Astrology? Mmmm, well, my best friend is studying astrology seriously. She's done charts for my last couple of solar returns as well as a couple of transit charts for me recently. The transit charts have all pointed to a lot of conflict and turmoil in my life during the past eighteen months; the solar return chart for 2001 basically said "BIG CHANGES" in the coming year -- a potential move, changes in the number of people I live with, and so on. At first I figured it was talking about my son leaving for college in a few months. WRONG! Six weeks later, I told my husband of twenty-two years, six months, and a day (but who's counting) that I was leaving and I wanted a divorce. Then I moved out of the family home, to live alone (more or less; the offspring is more with me than not, depending on his mood and whim) for the first time in my life. If that's not a BIG CHANGE then I don't know what one is.