I haven't gotten super far with my AST (....at all), yet, but I find I use the cards based on the people in my party.... and party-to-party situationals. So since I'm still not all that high, I'd just take my post as just examples x.x

Since I'm learning, also, more experienced AST feel free to correct me pleease :0

Someone mentioned in another post that they memorized the cards by association of the images - thats how I managed to memorize (and I have a shitty memory...)

Fire = Damage up..... BURN MONSTERS WITH FIRE +_+
Tree = Steady and hardy trees.... defense up
Blue vase = MP reqs lowered. ...I don't really have an association for this, but thats become a symbol for this card in itself o_O
Twirly Arrow = CD/Spell speed/Skill speed up - going so fast it's knocking things for a loop (the whirly/loop shape reference)
Spear = GCD faster........ *eats card* -_-
Orange jaggy = TP reqs lowered. I associate the rather violent looking jaggy lines with WARs overpower. And WARS eat TP. o_Oa WARs and Violence! \o/

For Royal Road....the light blue cards (not Ewer) I associated with "all the peoples!", whereas I haven't really differentiated between the effectiveness cards and the length extension cards, yet. Mainly because I tend to give Bole and Balance right away (tree/fire), so I'm really only left with the time extender cards (Ewer/Spire - mp/tp) to toss to Royal Road.

I usually find Spire (and Spear.) annoyingly ineffective for the lower level dungeons since nothing is really TP-expensive unless BRD/MCH is spamming AoE. I'll only use it when I have a WAR for a tank, otherwise.
I'll throw Ewer on DRK tanks (esp if they spam), or myself if I find myself going through MP like water for that run (but otherwise I sacrifice for Royal Road). I'll probably pass it onto co-healer WHMs/AST when I get it into 8-man content.
I use Spear most often as the sacrificial lamb for Royal Road. >_> (and Spire, sometimes.) As I've heard it only effects GCDs that -haven't- been used yet... and it's impossible for me to keep track of who used what and when - and if their GCDs are still ticking down (not effected by Spear).
Bole, I tend to use right away on the tank. I haven't hit a tank, yet, that couldn't benefit from a lil defense buff.
Arrow <3
Balance <3

Balance I'll use right away on DPS, as I feel tossing it to ROyal Road is an opportunity missed... usually either on the MCH to help them out, or to whomever I think might be spitting out the most damage. Sometimes I'll just change it up so one or the other DPS doesn't feel left out :x;
Same for Arrow.... though Arrow I'm a little more iffy on - depends on the situation. Sometimes tank if I see them trying, but having trouble with hate, so they can go through their enmity rotation faster, MCH or like Balance, whoever I think is spitting out most DPS. I haven't co-healed with a healer yet, but I might spend it on them, as well, if it's a cure spam race (seeing as WHM/SCH heals are more potent).

Generally, I favor Arrow/Spear's Royal Road effect to spread to everyone (ALL the Arrows! ALL the Balance! +_+ AAAHAHHAA-! @o@ *Maniacal laughter*), but I'll also favor the potency and length effect for Bole on tanks...

Every now and then I forget which card I had in Royal Road and use one ineffectively... .3. Thought I had a spear effect in ROyal and ended up spending Balance on.... just myself -_- (since I was targeted at the time) instead of spreading the fun...