The secret: it's not fast.
Your social life is a long term problem, and long term problems require long term solutions.
I can tell you what's worked for me (I've moved and had to start over socially twice). First, some principles:
All demographics are worthy leads
Don't discriminate based on age, gender, or attractiveness. There are two reasons for this. First: people lead to more people. People will invite you to things where you can find...more people! Second: this encourages you to socialize in "friend mode". A lot of people looking to build a social life skew their socialization toward attractive people of the opposite gender. That's stupid and alienating.
Be a regular
Meet people in neutral territory. You're not going to find success by going to a volunteering group once and inviting people to hang out outside of that context. Get to know people in your shared context and then take it out.
Find something: Rec sport, regular volunteering crew, dance class, a meetup group, etc. and then commit to it. Always go! You will make friends by accident.
Evaluate success via momentum
Don't ever evaluate your success by how many friends you've made. You can't control that. Evaluate your success by how many opportunities for friendships to grow you are creating. Opportunities can be expanded by doing more things, having a better attitude, etc.
The pipeline
Your potential friend pool is filled via a pipeline that has filters at these points:
Many people make the mistake of maximizing the output of filter 3, but this is not good because compatibility is an issue, and if you attempt in a small pool, you may end up with sub-compatible friends, or you may be discouraged by the failures in your attempts.
Instead, maximize filter 2. Meet more people. You can get a better feel for compatibility this way and more easily stay positive about the whole experience.
Conclusion
Create opportunities!