I would like to learn how to use it to advantage.
Actually, you might benefit from playing a game like the one I mentioned above: use the WorldBuilder to put the Cristo Redentor wonder in your first city right at the beginning of the game. Now you'll be able to experiment with switching civics without anarchy or the 5-turn delay between changes. Obviously, this isn't the same as being Spiritual, but it should be easier to get a grip on the different uses to which your civic options can be put.
I have never been able to use spiritual particularly well.
That's not unusual. It took me quite a while to figure out just how powerful this trait can be.
However, of all the traits, Spiritual is the one that most benefits from intensive micromanagement. If you want to fly through the game at breakneck speed, rarely pausing to manage your cities, then this may not be the best trait for you.
I try to avoid losing a trading partner or getting into a war on account of religious rivalry, (that way I can more easily war on anyone whose cities are near me and desirable) and so I avoid a lot of the religious techs, founding of religions, building of shrines.
I often do likewise. But, although most Spiritual leaders start with Mysticism (and so have a chance at the earliest religions), the trait has no overwhelming synergy with religion-founding. Having a religion is, of course, most useful - the religious civics are some of the best for anarchy-free switching - but Spiritual can work with most any strategy you care to devise.
I have a few civics that I use a whole lot (representation, mercantilism, bureaucracy, slavery) and once I get them I often want to keep them.
And this, believe it or not, is where Spiritual really shines.
For any non-Spiritual leader, there's not much choice but to stick with a set of civics for protracted periods, changing only when a new civic becomes available, or a different civic is desperately needed.
A Spiritual leader, on the other hand, can have his/her civics set up as you describe for much of the game (actually, slavery's an exception I'll come to in a bit), but also switch to different combinations for a few turns when necessary.
For example, imagine running a Specialist Economy with Representation, Bureaucracy, Caste System, Mercantilism and Pacifism as your 'standard' civics. Now, this lot are great for peaceful teching, but not much cop for war.
So, before launching a campaign, you can switch to Police State, Vassalage, Slavery, and Theocracy, and start pumping out more experienced troops at an increased rate (aided by judicious whipping).
Now, a non-Spiritual leader could do this as well, but at the cost of several turns of anarchy every time the switch is made either way. The Spiritual leader, on the other hand, can do this (virtually) whenever he/she chooses without wasting precious turns, meaning that short bursts of military production can be inserted amongst the more lengthy periods of teching and/or building.
This, then, is where the micromanagement comes in - you'll want to maximise whatever it is that your civics are boosting. So, in the military phase, you should switch from specialists and commerce tiles to hammer and food tiles.
Furthermore, Spiritual leaders can often make much better use of civics like Serfdom and Universal Suffrage. Since we don't have to stay in Slavery all the time (we can just switch to it for 5-turn bursts of whipping), Serfdom can be very useful, getting our improvements built more quickly.
To my mind, Universal Suffrage is one of the weaker civics in many situations. But the ability to rush buy units or buildings can occasionally be extremely useful. For example, newly built cities can very quickly be turned into powerhouses if a few key buildings are paid for in cash. Again, the Spiritual leader can afford to switch to US for a few turns now and then to take advantage of this, whereas a non-Spiritual leader will be discouraged from doing so by the lost turns of anarchy.
These are just a few of the tricks that can be pulled off with a Spiritual leader. I'll leave you to work the others out for yourself.
Edit:
KMad said:
same goes for religion changes people ask for. you can accept those demands and then change back 5 turns later but you keep the +.
Since KMad mentioned this, I'll add that switching religions (or out of religion) for a few turns can also be very helpful when you want to trade techs or maps with AIs who would otherwise think you a heathen. You might even be able to bribe them to war with one another! Hooray for Spiritual!!