"Plato believed that the state and the gods were associated, "Hence crimes against the state are crimes against the gods and vice versa. When a man kills himself without good reason… he is committing a crime".
[6] This allowed the state the right to punish. However, this did not imply that suicide was completely unacceptable. Plato believed that suicide was acceptable under some circumstances, similar to Socrates."
en.wikipedia.org
I believe suicide as a means to end mental suffering or poverty was seen as ignoble and unmanly in ancient times. Suicide to evade capture/enslavement/torture from an enemy was acceptable for men. For women, becoming a widow or having been raped thus one's honor stolen were acceptable reasons.
People were more acquainted with poisons in the past. In King Louis's France the time of inheritance powders arsenic could be bought but only by the upper class. In addition for use to murder, I wonder if anyone used it to ctb. Village herbalists or cunning folk would know what plants to use but likely guarded that knowledge for the same reasons people today are reluctant directly help facilitate suicide.
Cleopatra is said to have died by snake bite but there's some dispute that the may have done the puncture herself or with help and then rubbed the venom into the wound.
I imagine jumping from cliffs, drowning, fire, suicide by instigating unnecessary combat (old school suicide by cop) and poisoning to be common methods. Not much different than today minus technological advances like guns, inert gas, trains, cars etc.