It's the same as the original pokemon games, so any of the battle charts for the handheld versions will be accurate. Its important to note that each attack has its own type listed under the name, so like raticate is a normal type but his bite is a dark attack and thus effective vs psychic types etc.
The number to the right of the attack is how much damage it does. Lower damage attacks seem to have much faster animations and can be spammed very fast, where as like hypnos confusion is pretty high damage but the animation is slow so it fires less often. The blue bar on their special is how long it takes to charge, and how many stocks it can hold. Some are one big bar but do a ton of damage, others are 3 small bars but have lower damage values (you tap and hold your pokemon during a fight to use the special). Also worth nothing you can swipe left/right during battles to dodge attacks, not particular useful during the normal attack spamfest, but if you see the enemy use a big special its usually worth trying to dodge it, as the single bar specials are typically ~60 damage and pretty nasty.