So, this is my question, the feature assessinate said I has advantage when I make an attack roll again a enemy who hasn't taken turn yet, but this apply all turns or only in the fist turn after determine surprise and establish positions.

Assassinate

Starting at 3rd level, you are at your deadliest when you get the drop on your enemies. You have advantage on attack rolls against any creature that hasn't taken a turn in the combat yet. In addition, any hit you score against a creature that is surprised is a critical hit.

I has this question because I star playing since the last year and veteran players tell me this skill only works in that first turn, after that first turn the skill is totally useless.

Thanks for your time and forgive me for my broken english

At the beginning of combat if you go before them, they haven't taken a turn yet, so you have advantage. Once the creature has taken a turn, it has taken a turn and you don't get advantage from the feature anymore.

Yes, it is only useful on the first turn.

Thanks bro

Quote from YeissonD >>

So, this is my question, the feature assessinate said I has advantage when I make an attack roll again a enemy who hasn't taken turn yet, but this apply all turns or only in the fist turn after determine surprise and establish positions.

Assassinate

Starting at 3rd level, you are at your deadliest when you get the drop on your enemies. You have advantage on attack rolls against any creature that hasn't taken a turn in the combat yet. In addition, any hit you score against a creature that is surprised is a critical hit.

I has this question because I star playing since the last year and veteran players tell me this skill only works in that first turn, after that first turn the skill is totally useless.

Thanks for your time and forgive me for my broken english

If you get surprise, which is incredibly rare, the ability comes up on the first and second rounds, because surprised creatures don't get a turn round 1.  It will never come up on turn 3 or later.

I find procing the ability is actually pretty rare as it requires:

1. You to surprise the enemy.  Depending on all the factors at play this part probably happens a fair amount but rarely ever what I would call "Consistently" but this is my experience.
2. You have to roll a better initiative than the enemy as surprised ends after their first turn in combat.  If you roll low even if you surprised them the ability no longer works.
3. You have to hit.  Granted you get ADV on the roll but if its a high AC enemy then its decent odds you will miss and you basically get one shot most of the time as a rouge to hit. 

Overall it's just not that great of an ability and I generally connect it to a skill and have them able to roll it as a contest against the first enemy they attack on their turn. 

Depending on how they want to do it they could roll deception if they want to feint and strike from an unexpected angle,  Sleight of hand to make them not see the dagger in the other hand,  persuasion if they are going to convince them to put their guard down, or even acrobatics if they want to flip over them and hit a vital point.   

They do not get a full on crit for the sneak attack but they get PB# of d6 extra damage to the attack and if they crit naturally this is included in the doubling of the die of course.  

This is my homebrew solution of course. 

Quote from quindraco >>

If you get surprise, which is incredibly rare, the ability comes up on the first and second rounds, because surprised creatures don't get a turn round 1.  It will never come up on turn 3 or later.

 No this is wrong. Of course they get their turn, they just aren't allowed to act during it.