I just started playing Ys I, after letting it sit down on my library for a very long time.

I chose normal difficulty; as soon as I left the first village I was greeted with a simple tutorial explaining the bump system and how I should focus avoiding straight contact with the enemy.

With that said, how does the damage works? Honestly I'm having hard time with the game; the first enemies seems to be some kind of walking trees with a club, to which I deal very little damage, while when they hit me I lose a good chunk of health.

How should I approach enemies? Hit and run tactics I hope not)? I also tried to attack them diagonally, but i end up getting hit anyway.

Any help would be appreciated, thanks in advance :) .

Generally it is a kind of "hit or being hit" style system. You deal damage whenever you bump something your character face. The same is true for the enemies also, and by bumping an enemy that face toward you is basically like running into an attack. You have to rely on agility, trying to outmaneouver your enemy and bump from the sides or back. It is pretty hard sometimes and there are times when you have to farm a little with weaker enemies before you will have a chance against the stronger (stronger enemies usually turns pretty fast compared to you).

Usually when you change direction fast they will not follow you instantly giving you time to attack them diagonally. This is the advanced strategy which is pretty hard since if you're not enough fast or you do it with a wrong angle they end up counterattacking you dealing heavy damage like you said.

The easiest way is abusing the range and wideness difference. The enemies usually doesn't cover their full face. There is a little space at their left and right side from the front. Running toward them while aiming to those points not trigger them to turn toward you. But as before you have to watch out the speed difference since from very close range their angle is no longer faceing toward you thus they will try to turn. If they are more faster than you this will cause no problem for them.