I don't think anyone has said this, but making friends when we're older takes time, patience and commitment - friendships don't just happen by chance or instantly!
If you 're really serious about this and fully understand how important socialization is to us as we age, then make it a priority. Find a club or a group in your area to join that you have some interest in. Go regularly - that is so important - introduce yourself whenever the opportunity arises, and ask people about themselves, how long they have been coming, what interests them most about the group etc. By being interested in the people around you, conversations flow more easily. Listening - really listening is more important that talking about yourself and your own situation.
Finally, the most important advice is "be patient" - it takes time to be gain acceptance as the new person in the group! Many of those people have formed good friends within the group but if you wait your time, genuinely enjoy participating in whatever the club or group is trying to achieve and go regularly, then friendships it will gradually happen over time!