Before You skill train:
Often Skill training takes a lengthy time to finish. To do it efficiently and effectively, you probably will not kill monsters, thus finding less loot in general. Some of the gear you will likely want includes unbreakable gear (head accessory, back accessory, rings, necklace, shields for example) that provides you needed stats such as MP & AP regen, and optionally MP & AP Drain. Still, it all depends on what you are training, and how you approach the training that determines what is needed at the time being. Extensive Skill training below level 20 is generally difficult because some of commonly used regen equipment is level 20+.
You will also want to have a sacrificial pet that dies easily (so that you don't have to waste time ending its turn), and you will also want to speed up battles by clicking the button until it says Normal (top right corner).
Training All Weapons
No matter how you look at it, leveling up all weapon/fist skills will increase the base damage the attack does to monsters. You will first have to survive the monsters attacks and this can be done through the following: Hp Regen, and resetting your stats for 5 paragons & investing in defence. Since you want to be efficient, you want to deal the least amount of damage and gain the most amount of exp per time period. Weapons generally break overtime, so carrying multiple weapons can help with skill training. If the monster you are farming is almost dead in battle, you can always run away and re-enter the battle to continue farming without killing the monster.
Training Divine Blessing
Requirements for Divine Blessing Magic: 6 Mp regen per turn
Useful things to have: Sacrificial pet, MP Draining tools (like potions or equipment with MP drain), Mystic Swamp Dungeon Unlocked (or a skull pixie)
Setup: Summon a pet and have it die, find a battle with 1 skull pixie (if its in a group, kill all but 1 skull pixie), drain that skull pixie's mp to 0 (through potions, gear, or wasting turns), and then continously use soothe wounds on yourself for 3 exp per turn. When a skull pixie has 0 mp, it will not attack, thus saving you time. The first room of Mystic Swamp Dungeon often has skull pixies.
Training Frost Magic
Requirements: 10 MP regen per turn, 4 AP regen per turn, lvl 12 frost magic
Useful things to have: Sacrificial Pet, Mystic Swamp Dungeon Unlocked (or a skull pixie), MP draining tools
Setup: You will have to level up frost magic to 12 first, probably most effectively done by finding a monster 2 levels above yourself, and attacking it with ice shard. You can run away as many times as you like to avoid actually ending the fight to continually farm the same monster grouping for skill level exp. Once your frost magic is level 12, you will unlock imbue ice, a self buff move.
Like Divine Blessing training, you would summon a pet, have it die, then find a skull pixie @ Mystic Swamp. Drain the MP off of the skull pixie, and then continously use Imbue Ice on yourself for 3 exp a turn. Room 1 of Mystic Swamp often has skull pixies, and skull pixies won't attack if they are out of MP.
Requirements: A shield, 4 AP regen a turn, Lvl 5 Shield
Useful things to have: Sacrifical Pet, Mystic Swamp Dungeon Unlocked (or a skull pixie), MP Draining tools
Leveling up shield to 5 requires you to first block hits with a shield, @ lvl 3, use shield bash to faster lvl up shields. Once you reach level 5, you will unlock shield brace, another self buff move which can be paired with the Mystic Swamp Dungeon training technique.
Summon A Pet, Have the pet die, find the skull pixie @ Mystic Swamp Room 1, drain the MP from the Skull Pixie, then repeatedly use Shield Brace on Yourself.