I think I would start by finding something you love to do. Hiking, playing bridge, cross stitching, gardening, political campaigning -- and then find a local group that does that. I would rather start in that end than, say, join a group for single people (that's what I hear from my girlfriend who's been single for a long time -- she feels like those singles groups are more like a meat market). Worst case scenario, you won't find anyone you click with but you'll be doing something that interests you in the meantime.
When I look at how I met friends, it's largely through work. When I was single and working full time, it was either through work or through kid activities (and because I'm an older mom, the second didn't work out for me -- the moms who had kids my kids' ages were in their 20s or 30s and wanted to go clubbing; not my scene).
I don't have many friends and I have to admit that it's definitely for lack of trying. I'm more guarded; I'm also pickier, and I simply haven't felt like making the time investment was worth it, compared to what I could be doing with my time.
But if I did, that's how I would approach it -- joining a club or class or organization that does something I enjoy.