"So how do you figure which religion is the correct one if there is indeed a correct one?"
The answer to this is simple. You get down on your knees and ask God Himself. It helps a lot if you pray in the name of Jesus Christ. If you approach this method with a sincere desire in your heart to know, He will lead you to the correct answer.
I searched for seven years before I even asked the question. I didn't know that I needed to ask. In my case, I had been attending one Church after another. My quest began when my family was moving and my mother stopped in the middle of packing and said, "When we move, there will be a lot of churches there, and we need to find the right church for our family." I had what you might term a spiritual experience and I knew that was my responsibility. I was 12. Before then, I did not realize there were "a lot of churches." I didn't have many opportunities then, so I probably visited only 6 different churches during that period.
My quest began in earnest when I left home to go to college. But as I visited different churches the Spirit would say to me, "There is no light here." One Church I visited, I was not permitted to advance to the door to enter. I could move, but not to the destination I had intended. I attended one particular church for quite a while when the Spirit said to me, "You don't belong here." So I responded, "Then where do I belong?" Several months later, I attended another Church and the Spirit said to me, "There is light here." To be honest, I didn't know what that meant. I thought it meant physical light. Now I know that truth is light. It takes time to know things, to be taught correct principles, but it starts with faith. Faith is the substance of things hoped for, the evidence of things not seen. Just wanting to know is the beginning of faith. So if you really want to know, you go to the source of all knowledge. "If any of you lack wisdom, let him ask of God, that giveth to all men liberally, and upbraideth not; and it shall be given him. But let him ask in faith, nothing wavering. For he that wavereth is like a wave of the sea driven with the wind and tossed."
When God lets you know which religion is correct, that doesn't mean you will receive all the answers at once. You still have to operate on faith, but knowledge unfolds to you in an appropriate timeline tailored just for you. At some point in your journey, after you have proved your faith through trials by obedience to His commandments, He will reveal Himself to you and you will know for yourself that He exists, and you will come to know Him better. He is not to be proven to you before you will follow Him, because the purpose of mortality is to gather those who of their own free will and desire wish to serve Him and live in accordance with those sets of societal principles which have been tested and which actually work.
When you ask which church is correct, you may be led, as I was, or brought into contact with those who will be able to begin to teach you correct principles. This is so you have the opportunity to begin to exercise faith. There are people who are always praying and asking to be led to those who are searching for truth. As I was taught, I received an impression that I should accept their challenge to be baptized, after which the Holy Ghost was conferred upon me. Once I had the gift of the Holy Ghost, I could learn faster and truths became more understandable.