Now, before we get into this, there are two things you should know about: IVs and EVs. IV stands for Individual Value, and is a value from 0-31 that determines the stats of a Pokémon. Each Pokémon's IVs are determined when you catch or breed it, and can't be changed. Pokémon have one IV for each stat, so one Attack IV, one Defense IV, and so on. IVs are what make each Pokémon unique, and why two Pokémon of the same nature have completely different stats. (IVs are like a Pokémon's genes; everybody's different.) IVs also determine what type attack the move Hidden Power will be. There's a glitch in Gen III where roaming Pokémon will have very low IVs, which affects Latias in Sapphire (but not Emerald).
EV stands for Effort Value. Each Pokémon starts with 0 EVs, and gets more as they battle other Pokémon. Each Pokémon is worth a certain number of EVs; for example, Latias is worth 3 Sp. Def EVs. A Pokémon starting with 0 EVs that defeats a Latias in battle by itself will end the battle with 3 Sp. Def. EVs. 4 EVs in a stat equate to one point of stat growth. Pokémon can have 510 EVs overall, with 252 per stat.
Generation VI greatly simplifed this whole process by introducing Super Training, allowing players to train for EVs more efficiently, and without having to know which Pokémon are worth what EVs, and so on and so forth. (Let me tell you, it was a pain in the ass before then.)
So, what's the best way to train a Latias? Full disclosure: I'm not into competitive battling, I mostly just battle against the NPCs and whatever the current gen's version of the Battle Tower is. If you're looking for competitive strategies, spend some time at Smogon. As a Legendary Pokémon, Latias does come with some caveats: you can't use the Soul Dew in competitive play (whether in tournaments or in the generation's version of the Battle Tower), but Latias is still quite useful.
nature & evs
Actually getting a Latias with the nature you want is the main reason you want an Eon Ticket (and why not having one can be very frustrating). Because the nature of roaming Pokémon is set when you start your game, you're stuck with what you have. I'm not actually sure how it works with the Latias you get in Alpha Sapphire; if anyone knows feel free to let me know.
In any case, Modest (+Sp. Atk, -Atk) and Timid (+Spd, -Atk) are really the only natures you want on a Latias. Those are the two stats you're going to be using, and you want to boost one of them depending on your moveset.
There are a lot of different EV spread options for Latias; in this case, I'd honestly suggest looking over Smogon and deciding from there what kind of EV spread suits the moveset you're going to run. Latias's worst stat is her HP, so it's not a bad idea to put some EVs in there to boost it, but boosting her Sp. Atk and Speed are also worthwhile.
So this is the set I used when I last actually used Latias: in Emerald, against the Battle Frontier. It's a little dated, I know, and Solarbeam in particular may seem like an odd choice, but when you've only got 12 moves across your 3-Pokémon team, it's hard to cover all your bases. Still, it worked well for me back in 2005. Now if only I'd known the Soul Dew didn't work there! (The game never tells you.)
This is a more modern set for Latias, and one I'd suggest running today. Latias is an excellent Defog user given that she can switch into most traps thanks to Levitate; Roost allows her to heal, and the other two slots let her take out the offense. Psyshock is an alternate for Thunderbolt if you'd rather use her Psychic-type STAB. Be warned, however, that you can only actually get Defog in Gen IV; without it, use another attacking move or Calm Mind.
As a Legendary Pokémon Latias has a great moveset and tons of options, and now that she's got a Mega Evolution those options have only increased. Check out Smogon to find out different ways to use her.