Team Building 101
So you're sitting there getting blown up by a dumb Flammie in one of the early dungeons and you're like "what the hell?" Well, with one look at your team roster, no wonder you're getting slammed! Early on, it's difficult to scrounge up a skeleton crew much less a super kickass army, but I did well cobbling the following team together:
Your starter dragon. There's a reason why they gave him to you for free, you know! Its leader skill also incentivizes you adding monsters of the same element to your team, so do that.
Your rare pull. Unless you got a super rare one and your team cost isn't high enough to equip it lol
An attack/technique monster: Gotta get that damage in! Try to have it match the element of your leader.
A healer. If you didn't get one of the five sisters from the rare machine, they also drop rarely as the bosses of some of the early dungeons. The 2* form of Carbuncles, as creepy as they look, also do in a pinch.
A 2* blob monster. All of them have orb changing skills when evolved to 2*, and like Carbuncles, require relatively easy to acquire materials to evolve.
If you get something better out of the Pal or Rare machine, obviously swap those in where appropriate. Once you reach harder dungeons, you'll need to start specializing to deal with the specific hazards within. What strategy you want to prepare for those depends both on what monsters you currently own and what you're willing to put up with to fill holes in your team. Post your troubles in the thread and we'll try to help you out.