I think most cavalry FAQs out there already gave very good detailed strategy about how to make good use of the cavalry. I took their advice at heart and found my Cavalry become my main attack force. All my army stacks consist of mainly cavalry (equates, I'm playing Rome) with one infantry (or two if I plan to use my army to face an army with size close to a full stack) no archers and no skirmishers (velites) plus one onager for attacking city wall. Often time, my infantry has only limited contact with the enemy force.
With cavalry I can usually wipe out all the infantries (from weak warband to hoplite phalanxes) with minimum (or no loss if the infantry units are not heavily banded together). Against cavalry units, I also usually get them into "shaken" state very soon once I engage them.
To me, there is one and only one way when using my cavalry: attack the enemy unit from rear and flank.
My strategy: Divide and Conquer
Because my units are mainly cavalry, I can't go head to head against the enemy units directly. Thus I try to engage them section by section.
As I said, the only way to engage any unit with cavalry is from rear and flank, here's how you get into the position.
To get to the rear or flank of a cavalry, you need to have at least one unit in front of them to get their attention. Usually, it's less likely you can directly position your troop by putting one cavalry in front of the enemy and others at its rear or side. Because the enemy cavalry may be deep in its troops. Generally move one cavalry slowly to the edge of the enemy to lure some small number of units (if they are not already charging to you) out while having some attacking cavalry units at the far sides of this decoy unit and be ready to charge.
Once you get some enemy units moving forward, lead them some more distance by pulling your decoy cavalry back (walking if possible to keep them on hook) to be further away from the rest of their idle units. This also helps to position your waiting cavalry units to be at the side of the enemy units. Then charge the side cavalry into the enemy units. Always pay attention to the direction the enemy units are facing and never charge into an infantry facing you, that could be a disaster. But for archers or skirmishers, there's no need to concern.
If the enemy units are cavalry, sometimes you may need to also charge your decoy unit back into the pursuing enemy cavalry if they will reach your decoy unit before your attacking cavalry units can reach their rear/flank first. Because when an enemy unit reach your cavalry's back, they can easily wipe out over half of your unit fast. By charging the decoy unit back into the pursuing cavalry, at least the impact won't be that much, you sustain much less loss. Either way, once your attacking cavalry reach the enemy's flank or rear, it's a sure victory.
With this strategy, one unit of equate (size 27) can take on one unit of any enemy force (warband, hoplite phalanxes of size 60) at a time easily.
Yes, there are lots of micro management here and I pause often once my units engage the enemy. It's vital to avoid charging into spear heads at all cost. But with this strategy, I can keep my army size small with lots of army units. Most fights I encountered, the enemy size is always much higher than mine and sometimes the number could be close to 2 to 1. The result is always that I have a minor loss with the enemy army fully wiped out (I always continue fighting when prompted). I get "crushing victory" oftentimes so I don't put general in my army anymore (I leave them to be governors to grow my cities). In every one or two battles, I have my captain promoted to be a general because the crushing victory. Thus I'm spreading generals to all my cities.