Deduce where monsters are and kill as few as possible. If you need to scout, kill weaker monsters to reveal squares over stronger ones. Learn the secrets of each of the monsters. Your first objective is to explore the full board so you know where everything is, and can secure all the loose experience, especially the gnome. You want to preserve your HP as much as possible while doing that. Calculated risk and deduction. If you play perfectly, you will end up with 13 hearts left over, which doesn't sound like a lot of wiggle room, but its only the difference of using HP scrolls sooner rather than later, so if you need to use a scroll at 6 hearts instead of 9, you're only losing on 3 hearts of that extra wiggle room. And if your only objective is to kill the Dragon, you have TONS of extra space if you're still getting the hang of the game.
Long story short, do not try to kill everything. Not right away. Start by just fully mapping the board, and it will get a lot easier for you. Find the exp chests, the egg, isolate the gnome, and hunt down the rat king, slime wizard, and eventually the mine lich. Then once you've done all that, start killing things until you're out of hearts, level up or use a scroll if you can't, and repeat until you have 13 hearts to kill the dragon with. Or more if you want to aim for the full clear.