Linda, Here are some other to make friends:
1) Ask people questions about themselves. OMG, people love this – they love talking about themselves and will think of you as a great conversationalist, even if you’re really just asking questions and listening.
2) Keep your conversation (at first) light and genial. Try not to be negative too often.
3) Reciprocate – if a friend invites you out for coffee, invite them to do something at a later date. It doesn’t have to be the same thing – they could take you out for a fancy dinner, and you might prefer to have them to your house for a glass of lemonade. Whatever! People want to feel wanted.
4) As Penny said above, figure out what your interests are and go to places where people do those things. Meetup.com has lots of groups for like-minded people to make new friends. Volunteering is another great way to find friends. If you belong to a church or other organization and it’s hard to meet people there, see if they offer smaller groups within that organization so you can get to know a few people. (I belong to a giant cathedral and never made friends there until I started volunteering in the bookstore once a month – I meet tons of nice people all the time!
I was a shy kid, and my Mom pushed me a little to get outside of myself, and the “asking questions” thing really started me on the right track. Best of luck to you!