Question about curses..

Hi I'm quite new to the game and still figuring stuff out. My question is, if i have a gem setup that is: arc brand/wave of conviction/flammability.
Is in this case, Arc brand the spell I will use, and will the latter 2 trigger of me using Arc brand??

Thanks in advance!!

You need the Hextouch support gem for a linked curse to be applied alongside your attack/spell.

For example: Arc - Hextouch - Flammability would apply the curse to every target hit by Arc.

You can use a different skill linked with a Cast when Damage Taken (CWDT) support gem plus Hextouch to automatically deliver curses when you take a small amount of damage. A popular setup for that is:

Cast when Damage Taken (lv 1) - Storm Brand (lv 8) - Hextouch (lv 20) - Flammability (lv 20)

CWDT will trigger Storm Brand when you taken around 150 damage, and because Storm Brand is also linked to Hextouch, it will deliver the linked curse (Flammability) to every target it hits.

Notice the levels of the gems: CWDT is at level 1 to be triggered by the smallest amount of damage possible; Storm Brand is at level 8 because it is the highest level it can still be triggered by CWDT lv 1; and the other two gems can be at any level (in fact, the curse gem NEEDS to be at a higher level), because they shouldn't be triggered by CWDT, but by Storm Brand.

That said, you could look into buying/crafting a glove with the Curse on Hit affix, which will skip all this nonsense and just apply whatever curse it has affixed on every attack you do.

EDIT: also, keep in mind that Hextouch doesn't work with Mark curses (like Assassin's Mark or Sniper's Mark). It took me a while to notice it didn't (it used to, but then GGG changed it a couple of patches ago).