Haha, It is hard to say exactly how one builds up a friends network in a particular living location. When I am a long-stayer, I always make it clear that I am staying in a place for a long time, not just a two week tourist. It makes a big difference.
Here are some quick ways I have found expat and local friends and I have tried to add specific examples:
* I have made expat friends at hotels that I stayed at or even meeting at restaurants that sort of thing. I am having lunch tomorrow with an American who saw what looked like a fellow American at the supermarket and introduced himself to me (since there are not many foreigners here). We have gotten together a few times since then. I met another guy through him who then gave me the phone number of a local expat looking for a tennis partner.
* I have made many local friends through expat friends. Expats that have lived in a place for years have built up their own network of friends. This is probably the fastest and best way to meet people.
* I have met many people through couchsurfing.com. I have used this mostly when passing through as opposed to living in a place. I did this in Medellin 2 years ago on my first visit here, and my current girlfriend is the cousin of the girlfriend of the American guy I contacted through couchsurfing.
* I have met a lot of people through girlfriends (I have had two girlfriends abroad since I retired and one other relationship that never really got to the girlfriend stage). I do often honestly wonder if it will be much harder for me to meet people when I get much older. Also, I wonder if my whole travel experience would change for the worse if I were married.
I am going to hesitantly and somewhat immodestly add a comment here to bring some context. A number of my friends sometimes call me "Kavorka" from the aptly named Seinfeld character Kramer, because I seem to attract women for whatever reason: Cosmo Kramer - Wikipedia, the free encyclopedia
In "The Conversion" after Kramer attracts the attention of a young Latvian Orthodox novice, Roberta, he learns from the priests that he has the Kavorka
(lure of the animal)
I am just trying to say that my experience would probably not have been so positive if I were an old, bald, fat guy. I only reluctantly add this, don't mean to be boasting or anything.
* I keep in touch with friends worldwide, both locals and expats. I have time and motivation to do this since FIREing. On a weekly basis I will typically exchange a fair number of emails with friends and online chat with some friends in the Philippines (they seem to prefer chatting). A good friend there wanted to chat last week when her dad was in bad health this week and I made myself available. Her dad died two days later. Another friend is looking for a job and I have given her a lot of encouragement and pointers. I have never sent money to anyone, and no one has ever asked (oh wait, one girl I met in Thailand did ask for money via email in 2008, just say no!).
* I play tennis, I run, and keep in shape. I meet friends doing this and I also do it with other friends. In Thailand we would regularly get together for tennis. I did joint running workouts for over a month with a personal trainer on vacation. And this year I had a regular running date with a couple of different friends every other day.
* Some local friends want to learn or practice English with me, and that is fine with me. I do pay sometimes when I go out with some poorer local friends. I met a nice girl in Manila, strictly plutonic relationship, and she lives in a small house with 9 other family members. We have met on each of my trips there. Usually, we go to several places together and I pay 100%. If I didn't pay, we really could not spend time together. When they had the typhoon there last year, their house lost the roof. Then she had to stay at a friend's house for several weeks because there was not enough dry space on the floor at her family house, they gave the people with job sleeping space priority (she was attending university). She always wants to introduce me to her beautiful girlfriends.
* I have made friends with a lot of fellow ERs and expats over the internet, mainly people that I "knew" through internet forums, and then later met up with them. In fact, I highly recommend this.
* Today I had to go to Colombian immigration for an extension of my visa. I met a missionary from Japan there, he has lived in Medellin for 4 years, and we plan to meet up again soon. He speaks fluent English. I asked for his number instead of just leaving without exchanging contact info, and then found out he lives just 2 blocks from my girlfriend and just 1.5 kilometers from me.
* I have just randomly met people. I spent a week on vacation with the family of an elderly lady I met on the street in the Philippines. I still contact them when I visit the country. Her son named his first son after me. I am not really very good at meeting people this way, and I am more cautious nowadays for safety reasons, but it happens sometimes.
* I have made a number of friends at language schools (as a student), both fellow students and teachers. And also through my Thai tutor in Chiang Mai I met some Thai locals.
So what I find is that when I have more time, I can make more time for friends. For me, at least, working would take away from this, just like it did in my working career.
Let me add one more thing. I am more careful about the friends that I make now. There are a lot of odd expats, much higher percentage than in the general population
Be careful out there!