"I prayed for something and it happened. How does that work?"
Then you are one of those blessed with a reality in which fate may blatantly weave events. The more accepting you are of divine predetermination, the more it may permeate your reality. You don't need an explanation or functional model as much as acceptance. You could even believe in no predetermination and instead that deity(s) actively dictate events on the spot. Whatever your reason, or lack therof, divine occurences are acceptable in your reality. Your path is one of magic.
"So should I pray more?"
That is up to intricacies of your belief system. If your divinity involves belief in your subconscious, based on neurons, being involved, then yes prayer does activate neurons and is known to do so in an unusual hemisphere in an unusual place. So prayer IS something special. You could attribute many concepts to a prayer and subconsciously trigger the linked concepts upon praying the prayer regularly. Mantras such as Am Mani Padme Hum function similarly. These are healthy continuous prayers.
As far as praying for a specific thing and it happening, are you placing something into reality for reality to align to? Are you praying to an entity(s)? How vague can you be? Is divine love for your guiding force(s) appreciated? Prayer is a big world and alot of it is dependent on you. Should prayer be part of your spiritual path, it is a journey tailored to you for you to explore. Any external telling of 'how it works' is only a sharing of what that entity learned from their own journey; and only relavent to you if you wish for it to be.