The main "practice" in Unitarian-Universalism, unfortunately for you, is the discipline of being part of a congregation--volunteering, helping out, doing social justice advocacy, dealing with the wide variety of viewpoints you're likely to encounter. It's a very this-world focused faith. CLF (Church of the Larger Fellowship) is a good starting point, but you might find some like-minded people and start a book club/discussion group. Depending on your interests, there are several Beacon Press (the UU publishing company) books to read. You might wind up starting your own fellowship.
For most people, the classic "starting out" book is A Chosen Faith: An Introduction to Unitarian Universalism by Forrest Church and John Buehrens.
If you're coming from a Christian background and want an idea of what some UUs think of the Bible, read
Understanding the Bible: An Introduction for Skeptics, Seekers, and Religious Liberals
also by John Buehrens.
If you're deeply disappointed in supernatural religion, and are drawn to reason but still want spirituality, a great book by Galen Guengrich is God, Revised.
If you want to start with historical roots, you might read "The Unitarians and the Universalists" by Robinson. This is a pretty thick tome, not for everyone, but it tells the story from the beginning. Most UUs aren't that aware of the rich history that led to where we are. Coming along the history might parallel your own spiritual path.
The YouTube channels for All Souls in Tulsa, OK, and All Souls in New York City offer dozens of great sermons; try watching one or two of these each Sunday if CLF isn't in your time zone (and CLF offers an online option, doesn't it?).
As far as a "prayerbook", get a copy of the UU hymnal, Singing the Living Tradition... the readings in the back are quite good if you're looking for a solitary spiritual practice. The words to the hymns--especially the "UU words" to hymns you might be familiar with in a Christian church--are also a great source of insight.
That's what strikes me at the moment...hope this helps you find what you're looking for.
