Aside from the only free autoskill you get in the game which is Enchant Weapon buff , other autoskills can be manipulated through equipments and crystals.
Enchant Weapon - you get this skill when you become a full Enchanter at lvl 140 and can be upgraded with a skill book at lvl 200.
This buff will give you the chance to trigger 1 random element autoskill(Fire Lance, Ice Spear, Thunderbolt, Earthpike)when you attack.. This the only autoskill that can be seen in your party's log..
Every other autoskill damage that you manipulate will only be seen by you in your battle log.. Other players will see the animation of all your autoskills but not its true damage..
Now for the other autoskills, there is a wide variety of equipments and crystals to choose from but I will tell you only of what i use..
Fire Element:
Weapon- Pramia/Gerust .. Pramia has Fire Lance autoskill which can be triggered by attack.. Just put a Gerust crystal to further increase your autoskill damage.
Armor and Add Gear- any armor or add with autoskill% works though i would suggest DPR up for armor and Spin Shield for addgear.. Put an Ifrit crystal(add fire lance autoskill to ur attacks) to both of them and u 2more fire autoskills.
Special-you can go for reduce bangle or boost ring for an atkspeed buff to further increase the chance triggering your autoskills..
with this setup , you can trigger up to 5 autoskills with one blow. 3 Fire Lance from pramia and ifrit xtls.