For free, how can I find out if I have inherited money from someone close to me that has passed away?

You go down to your local Probate court and see if a will has been filed. But, if one has been filed and you were included with a bequest, then you would likely have been notified.

Often there is no way, even a paid way. When someone dies, the will goes to the local probate court and they will do some attempts to find you if possible. But then sometimes one relation does not file the will in court and tries to cheat everyone, so not even the court knows of the will. And so on. So you need to know whose will you may be listed in and if they die, check the probate of their estate.