There are many ways to make friends, being invisible is not usually one of them. Most of the people you see with friends have gone through the risks of rejection by putting themselves out there. Here are a few pointers you may find useful.
1. Don't be too over zealous, but say hello to people here and there. There is no need to have deep conversations at this stage. Just be casual and nonchalant.
2. Remember that the topic of discussion that people like most is, themselves. Don't be too personal, but it's ok to act interested to some degree. Talk about their teachers, classes...etc...
3. Smile and let everyone see that you are a well balanced individual without any emotional friendship baggage. Most people don't want to be around others that will drag them down.
4. Don't be invisible. There is no need to act out and get in trouble, but don't just blend in to the wood work. Wear cheerful clothing and speak up once in a while, even if it's just to ask a question. Let people know you exist. Yes, there is a risk that some might reject you, but such is the case with anyone who gets noticed.
5. Be a part of something. Most of the people that have a group of friends are involved in clubs, church and other events where they have had the opportunity to work, or play, together. Being a part of something with others automatically makes you similar to them and easier to befriend.
Please remember, like Bill said, you are not alone. There are many more people that feel the same way you do. Even some of those that appear to have all the friends in the world feel like they have none, just the same way you mentioned. Appearances are a funny thing. Sooner or later you realize that not everyone is how they, at first, appear to be.
Good luck! You will do great.