Use shyness to your advantage
Force yourself to go up and say hello to strangers at parties, meetings and gatherings. If you're very shy, think of yourself as a 'successfully shy' person, because you can still make new friends. Making the first move takes the pressure off other people, and most of the time they will be relieved that someone else has set the ball rolling.
The remote control is not your friend
Chances are, you will not meet too many new people sitting home alone watching TV and moping. You really have to get out more, but fortunately you do not have to be out until late every night. Why not test the water by joining a group of some kind that meets once a week?
What makes you tick?
Friendships are often formed between people who have a common interest. Just be yourself, and find some like-minded others. If you're sports mad, join a local team for training or competitions. If you want to help others, why not try volunteering? Look on the internet for organizations (Better not Dating Agencies) that cater for singles meeting at events rather than under the pressure of "Blind Dating" You will probably enjoy the event anyway, even if you do not meet anyone you want to team up with
There are evening and weekend classes on just about any subject you can imagine, and even if you do not hit it off with anyone there, you'll still be picking up new skills, and will have something interesting to talk about. University students are generally spoiled for choice, and can join all sorts of clubs and societies at college.
Be interesting, not boring
Even if you're in a new town where you do not know a soul, keep up with your interests wherever you can. When you do finally meet some new people, you'll have something other than soap operas to talk about. It'll make conversations more interesting if you can talk about something current, such as the latest film or gig you went to.
Pack your social skills
Remember to smile, and try to look relaxed (even if you're nervous as hell) when meeting new folks. Introduce yourself early on in the conversation, and take an interest in the other person's answers. Eye contact can be very important here. Ask open-ended questions that allow the chat to flow easily, rather than closed questions that are just going to be answered with a simple 'yes' or 'no'.
It's all in the follow-up
If you get on well with anyone, offer to swap email addresses or phone numbers, and keep in touch with them. As always, consider your personal safety with anyone you do not know very well, and do not rush into giving them your home address or similar details straight away. Do not just ditch your old friends either, drop them a line every now and again if you've moved away.
Sometimes it just takes a little time.
You will not find a new best friend in one afternoon. It can take a while to get to know people, so just relax and take it easy.