Play the story campaign until you're out of stamina, then roach into co-op quests until you rank up and get more stamina again. I would highly recommend clearing up to the boss your main team's element is at (crab in world 3 at minimum) before roaching into co-op. If you're stuck, try doing the EXP dungeon, which is the second option in the Events tab (left tab on the main quest screen).
Co-op System: Host always uses stamina, joiners use half stamina if they are following the host, and it costs no stamina if the host and joiners are mutual followers (friends). Full price if host and joiner aren't following each other at all, which you'll almost always want to avoid.
Co-op quests give boss tokens for each boss, which you can and should cash in for limited shop items that reset monthly (void shop basically). Recommended: Get the Character, Weapon, and Unbind mats at least (rainbow things, limit of 1).
In the party menu, the 2nd option (exp) also lets you unbind (the mat that it requires there is the unbind mat mentioned above). This is in the second tab.
In the party menu, the 3rd option is grid (mana circles). The mats for these drop from the elemental dungeon, which is the first option in the Events tab. You can also trade for them with boss coins.
Every day you get 3 bonuses per Event and per Coop, for 6 total bonuses. I strongly recommend you save this for the highest difficulty, since it doubles all drops; this is the dialog that pops up before entering or hosting a dungeon.
Boss shop resets monthly besides the welfare unit, so don't rush the welfare unit unless you need to.
Tips and Advice
Leader skills apply to the characters in your party (unsure about sub-characters), so try to keep them mono-element since the bonuses are quite large.
You can use sub-character slots as safe ways to level units, especially if you're joining easier dungeon rooms.
I would roll to fill out your roster, try to get a 4* unit in every element and then fill the rest of the main slots with 3* units. Sub slots are much more flexible.
Sub-characters use their skill when your main character uses their skill, so you can get some interesting combos with the right setup.
Power Flipper is the extra effect you get from flipping after 10+ combos, some leader skills buff this damage effect, such as Wagner [wf name="wagner"]. The actual effect varies depending on the "type" of the unit (Wagner is a Bow for example).