In my experience as a psychic medium, I have seen that when someone dies by suicide, their Spirit does go to the other side. They go to either a hospital-type setting for healing, or to a place of spiritual teaching and support, or to both places. Every time, I have seen the Spirit surrounded by guides - almost like an escort, with a guide on either side of them.
I find that I am able to communicate with them, but it doesn't happen as freely as with those who cross naturally or when it is their time. Once I've requested to communicate with them, it may take days for them to be able to come forward, whereas others can "arrive" immediately.
Spirits whose lives ended by suicide have also communicated to me directly that they are in a safe place, this place of teaching. Each time the message has been consistent. They state that they see now why suicide is not an acceptable option. They have been shown that their path would have improved, and that there were others around them here in the physical world who were here for support and assistance. These Spirits come to understand that they were never alone, despite what they believed in the physical plane.
Part of these Spirits' learning also entails showing them the pain of those who have survived them, especially the survivors' questioning and anger about the person's suicide. When in the physical form, the life of the spirit was not a burden, but then became a burden once they took their own life. It is the burden of grief and helplessness that is felt by the survivors and the unanswered questions that remain.
If someone is contemplating suicide, they may think suicide is okay because of how I have described the love and guidance and teaching for those who end their lives. However, please do not misunderstand my message. It is never, ever okay with the spirit world that we end our own life.
I have been shown that when we take our own life, we will have to relive our lessons in our next life in order to complete our soul's original intention for experience and spiritual development.