It is fairly safe to say that somewhere out there, there is intelligent life. The odds of life occurring on any particular planet or moon are not good at all. If life does occur, the odds of that life evolving into an intelligent species aren’t very good and, even if it does, there are all kinds of things that could cause an intelligent species to cease to exist.
However, given that there are billions of galaxies, containing billions of stars with planets it is nearly impossible that Earth is the only place with intelligent life. The odds of winning the lottery are notoriously terrible, but chances are if you buy hundreds of billions of tickets every week for hundreds of billions of years you will win many, many times (and turn your hundreds of billions of dollars into tens of millions).
Even if we assume that there is intelligent life out there though we still have to find it which, given our current technology, is going to be a long, laborious project. Think of it as picking up one piece of straw at a time, from a pile the size of the Sun and doing a full chemical analysis of it to determine if it might be a needle.
Finally, when the day comes that the chemical analysis tells us we are looking at stainless steel we might be disappointed. Remember that humans have evolved slowly, from amoeba to our current form a little change at a time over billions of years. We have evolved specifically for the conditions of the Earth, which have changed substantially over that time. Our extraterrestrial friends will have evolved on a different planet, under different conditions, over billions of years and we may or may not have enough in common to communicate or even recognize one another as intelligent species.
This video from Hank Green at SciShow doesn’t get into all of that, but it does discuss all of the things that must be in place for a planet to be “habitable”. Knowing this is only a first step, but it will definitely cut down the size of the haystack.