Friendships are one of the most valuable aspects of a good life, I think, and understanding how to make and keep friends is well worthy of consideration. The same qualities that allow us to make friends are often the same qualities that allow us to keep friends.
In order to make friends, you must be interested in other people. This needs to be a genuine interest in others, not a social pretense. If you are interested in the people around you, they will respond to you and want to be friends with you. This means that in conversation with others, you are actually listening to what they have to say, not just thinking about what you want to say. Someone who is interested in others is a good listener.
In order to make friends, you must seek a common ground. This is the basis of most friendships, I think. Common ground might be taking a class together or living in the same neighborhood. Common ground might be two people who both have red hair. Or it could be two people who are children of divorce. There are thousands of ways of finding common ground with another person, and this is how friendships often begin.
In order to make friends, you must be open and willing to share some of yourself. If you remain private and "closed," it is going to be difficult to make a friend. Friendship involves not just taking, but also giving.
In order to make friends, you must be willing to demonstrate that you like the other person. There is no percentage in playing hard to get when you want to make a friend. This does not mean you have to be overly-enthusiastic and try too hard, making too many plans too fast. You can and should start slowly with a friendship, letting it build gradually, but you really need to let the other person know you like him or her and enjoy the person's company.
To keep a friend, you need to remain interested. Friendship is built upon this. If you are not paying attention to what your friend has to say, and you do not show you are interested, you will not keep a friend for very long. Being a good listener demonstrates that you are interested, and friends value this quality a great deal.
Common ground is very important in the early part of a friendship, but less so as time goes on. For example, I remain friends with some people I went to kindergarten with, although we went to different high schools and colleges and live in different cities now. That common ground was enough to get us started, but in a strong friendship, it will not necessarily remain so important. Sometimes the friendship that loses common ground and dissolves was not such a good friendship to begin with. I have had many friends at various places I have worked. Some remain friends, but others do not. So, this all depends on the depth of the friendship. A good one will survive a lack of common ground later on.
Giving of yourself is just as important in maintaining a friendship as it is in beginning one. There is an expectation in a true friendship that you will both share your thoughts and feelings. If you do not, the other person is going to feel a lack of depth in the relationship. This doesn't necessarily mean saying everything you think and feel, but to make another person feel special and valued, you do need to share.
To keep a friendship going, you need to continue to make clear that you like the other person, that you value the friend's company, that you cherish the relationship. A compliment about the other person can do this. Just saying once in a while that you are so happy to be friends is great.
In summary, we get out of friendship what we put into it. When we are interested, when we look for common ground, when we are open, sharing, and appreciative, we can make and maintain friendships throughout our entire lives.