My journey from skeptic to believer was long and painful as I simply refused to accept that there were things which could not be explained. I had a number of personal experiences which were "paranormal" in nature but I eventually found a rational explaination for them. At most I believed that some of these occurrences were just coincidence, a series of quite common events that all happened to occur at once resulting in an experience that seemed to be more than the sum of all it's parts. There were strange anomalies, but nothing paranormal.
However I also had experiences which I could not explain and they, if you'll pardon the pun, haunted me. I would constantly go over these experiences in my mind trying to find some sort of rationale, stubbornly refusing to even consider a paranormal explaination. The big one was an invisible entity which I have written about here before. This thing looked a bit like in the movie The Predator when the alien has its cloaking camouflage active. I saw it walking in the yard and when I tried to get closer and investigate it disappeared from view, immediately after that I heard noises in the house and objects were moved and rearranged. It was the most incredible thing I had ever experienced and for years I insisted that there had to be a non paranormal cause.
In the years that followed I continued to have strange things happen to me and around me and I continued trying to debunk them. And still there were things that I simply could not reason away; a supposed haunted pool table where I personally witnessed pool balls disobeying the laws of physics, an early morning jogger who quite literally vanished beside me, a cat hissing at a door as it opens and closes by itself, ect.
Out of desperation I talked to a friend about his experiences living in a haunted house, I've shared a bit of that here as well in a post about cursed/haunted French doors. This guy is a science nerd so I wanted to know how he squared his beliefs in the paranormal with his love of hard fact. He reminded me of the words of Sherlock Holmes, and also Data from Star Trek, that; when you remove the impossible then whatever remains, no matter how improbable, must be the truth. So if an object seems to move by itself Newton's first law says that it's impossible for that object to have simply moved itself, therefore the improbability of an unseen entity moving the object becomes the more rational explaination.
Afterwards I began researching the paranormal and getting an idea of what kind of rules and behaviors are associated with various activities. I soon began to notice patterns and similarities that perfectly fit with just about every unexplainable incident in my life.
The only big outlier is the invisible entity. I'm still not entirely sure what exactly it was but I now know it was something real and that it was something paranormal. So really that's the event that turned me into a believer, it just took about 10 years for that change to happen.