'Tough' is in understatement as their methods were pretty much brutal and very painful: the conclusion of one of the foremost experts on suicide in Antiquity Anton van Hooff. He's a Dutch historian but his book is also available in English: From authothanasia to suicide: self-killing in classical Antiquity.
If I recall correctly the premier methods (at least those that were found in historical records) were sharp weapons, hanging and jumping. Poison was not used often and it wouldn't have been a pleasant death anyway.
It's a misconception that suicide was always approved of in the ancient world (Rome and Greece) but it was rarely illegal (in ancient Roman law only slaves and soldiers were specifically prohibited from killing themselves) and often thought of as laudable and honourable, at least in the case of the upper-class and especially in Rome. Patricians, generals and high ranking officials were pretty much expected to kill themselves if they were about to suffer a blow to their honour.
The most famous example is probably Cato of Utica: a Roman senator who opposed the upstart Julius Caesar (who defied the Senate's express orders to leave his army and come to Rome alone to stand trial, this resulted in a civil war) and known as a stoic philosopher. After all his allies were defeated he decided he did not want to live in a world in which the Roman Republic would in effect no longer exist (Caesar laid the ground work for the subsequent Roman Empire which was in fact a dictatorship although it wasn't presented as such,, if it wasn't for his murder he most likely would have been the first true emperor of Rome) and he stabbed himself in the stomach with his sword.
It seems this wasn't enough and his friends and doctors rushed to his side, a physician put the entrails back into his stomach but he pushed the man aside, tore open the bandages, quite literally pulled his own guts out and died of bloodloss.
He was revered by posterity as a hero and the prime example of Roman honour and masculinity (virtus).
It's quite strange how this moral view could have changed so drastically. That seems to have been the handiwork of the christian bischop (later named a saint) Augustine of Hippo who condemned suicide in his book The city of God. On in my view rather spurious grounds: the main one being the supposed condemnation in the Fifth Commandment (thou shalt not kill).