You cant really focus on one skill at a time and theres honestly no tips. You just kinda train them. You get 5 trainings a week and most just train all 5 at once and then it resets in 7 days, so if you train Monday 5 times you can train that horse again 5 times the following Monday. Its completely random which skills raise points and how many each training. Some a little, some a lot or none at all. Thats why there is no real skill to it. I always recommend looking at the wiki. It isnt completely up to date with the newest editions of stuff but it has all the basics. As I tell any new person, save your money and dont spend it willy nilly. There are several training centers that host training for 1 bit. Until you get a good source of income going, there's no reason for you to pay more than that to train. 

Whats also very important is foal training. While I dont recommend breeding for a while, until you have good established horses to breed, once you so get there, foal training is important. You should aim to complete foal training, to get the highest training boost. To figure out the foals potential training boost, or TB, add the parents levels together and divide by 10. This is why it is recommended that horses be bred at a minimum of level 50, so foals can have at least a 10 TB once foal training is complete. Higher TB is higher quality horses. Training foals is just the click of a button, and it takes about 3 hours before the next session can begin. So no strategy again, you just need to do them all before a horse ages up to 2, and there is plenty of time to do so so dont stress about it. 

And while I know you only asked about training, I also recommend new players to look at my bits making guide. Many newbies tend to get in over their heads and end up broke pretty quickly and trying to sell off very low quality crossbreed mutts that no one really wants, or even basic low quality purebreds. So give this a look over, build up some money and good quality horses and let us know if you have any other questions, here or in the Discord. Welcome to Horse Fable :)

I would recommend using the disciplines guide to choose which discipline best fits each horse you have, this maximises your chance of doing well in shows. I tend to check which horses need training every day and do all 5 trainings in one go so I can use all their energy on shows/careers on the other days. 

I tend to give my horses a primary discipline and a career instead of a secondary discipline so that they can make money without me having to pay show fees when I'm feeling low on cash. Especially starting out, and until you've got some training underway, your horses will probably have low PS and might not place well in shows - you might decide to keep training their discipline while using their energy in careers until their PS improves. 

I wouldn't worry about balancing your horses energy with their training - training is important to increase your horses stats, which helps increase their level (When you put them in shows), so I wouldn't ever prioritise shows over making sure their training is complete for the week - it's basically an investment in supporting your horse to bring in more money down the road.

(Also, I would highly recommend Maki's bits making guide! I found it tremendously helpful as a newbie!)