Hold CTRL to attack, or the attack button on a phone. Face what you mean to hit, because a swing goes the way you are looking.
The blow lands when the weapon does
The damage appears when the weapon comes round, a moment after you press the key. Anything quick enough to step out of the way in that moment gets away with it, and so can you: watch what a monster is about to do and be somewhere else when the blow arrives.
A fight plays the same on a poor connection as on a good one. The swing may be late, but it lands where it should.
Getting your health back
Health and mana come back on their own once you have been clear of a fight for a few seconds. A miss puts both of you in a fight as surely as a hit does, so the way to recover is to get away. A potion buys you time when you cannot.
Poison, fire and the rest
Some blows leave something behind. Poison keeps working after the hit and armour is no help against it. Fire burns, a cut bleeds, and a hard enough clout leaves somebody unable to move for a moment. Whatever is on you shows as a row of marks above your health, and while any of it lasts you count as fighting.
Not every monster is the same
Point at a monster and its name tells you what you are about to start.
Some are Elite: drawn larger, with far more health, harder blows and a much bigger reward when they fall. Think twice before you take one on alone. Others have a character that changes how they fight, so one might be hard to hit and another might hit like a door but be easy to dodge. Read the name, then decide. The more trouble a monster is, the more it tends to pay.
When somebody comes with you
Everything you kill together is shared out, and whoever lands the last blow always gets a share. Your party's names, levels and health sit over their heads, so you can see who is in trouble without opening anything.
After the fight
Whatever died leaves something on the ground. Walk over it and take it, or leave it. If your bags are full, the bank will hold the rest: gold and the bank.
Then try it on something that fights back properly: your first dungeon.