There are fears who use to be with us until the time we face it, being alone is usually a fear that starts while we are kids and it reminds inside our minds until we face the time of being independent, this action is necessary for a normal way of growing and of course it means also the first steps to get into an adult mind.
Of course there are two ways that fear of being alone can be presented on human life, the first starts by parents or brothers dependency since we are kids, we get comfortable with the idea of having a constantly company and attention from them so we start to feeling afraid when we get alone for the first time.
The other way about how the fear of being alone can be presented pass by the figure of lost someone who had live with us for a long time, like a relative, and even a pet, here we spontaneity feel a fear that is combined with a deep sadness, and of course these second condition is more difficult than first one.
For the first one the fact of start doing the things by yourself and making some good moves alone every day, combining it with a good plan for your life are enough motivation to defeat and forget the fear of being alone, here you just break a tradition and your brain starts to think independent.
On the second case the things can result more difficult but there are not impossible, first you need to find task and design a routine who will not allow you to feel alone or to give a change for sadness to take control. Here you need to go on for some factors, including spiritual ones like search God and Pray, and doing some exercise routine, and by the way find time to meet new people and friends.