How can an introvert Asian engineer like me make friends?

My advice is to strive for excellence and let the rest come in time. "Excellence" is a journey you can do alone, and it will make you feel better regardless of what happens for you socially.

Ok, so what does this mean? You mentioned you don't speak English well. So the obvious choice is to go to classes to learn English. Definitely do that! But also follow the path of excellence: teach others English. Go to conversation groups and try to help people as much as they help you. Read books and share your favorites with people there. Why do you like them? How did they make you feel? Become more thoughtful. Which English words are your favorites? Memorize your favorite passages and poems. This is going for excellence. It isn't easy, but it's powerful.

Why does this work? Well, it turns out people who love what they do are fun to be around. Now when someone says, "what do you do", you can tell them this: "I'm really excited about learning English. I've never had a chance to really focus on it until now." Then ask them what their favorite words are, and they will join right in. Your energy and love of what you are doing will be fun to be around and interesting.

So now you are learning English and loving it. Do more. Apply this principle to work (master an area, really master it), to exercise (join crossfit, a climbing gym, martial arts, or dance). Follow your interests most of all. Try to put yourself out there 100%. It will take time to find mastery, but as you improve others will notice your energy and be drawn to you naturally.

As someone who used to be a much more introverted person and have sense became more extroverted in the past few years. The way I did it? Pick-up artistry. aka Learning the art of dating and relationships. This not only helped me with dating and love life, but more than that I learned how to be the best version of me. Now usually when I am with friends that are extroverted I am usually the more extroverted one! the most helpful was the base of my growth and learning which was by a man in the pick-up world known as David DeAngelo. His videos called The Mastery Series was probably the most eye opening and influential group of videos I have ever seen in my life. It helped me to look at my own "holes in my emotional armor" and be able to fix them. I highly recommend these. I also found that it makes being able to sell much easier and better too. =P

Like any skill, I'd suggest this requires practice. One way I found as an introvert was to join Toastmasters. I don't have a big fear of public speaking—I can do it if I have to, but being in practice makes a huge difference. I've seen incredible improvement in people after 3 or 4 speeches.

Most clubs will have a social aspect and might gather for drinks afterwards. It makes a good way to practice smalltalk and keep in touch on a regular basis. There's usually a mix of people... some will be struggling with shyness and fear of speaking, others may be naturals and make good people to study for technique.

I've fallen out of regular attendance lately, but I'd highly recommend Toastmasters.

I just finished reading the book "Quiet: The Power of Introverts in a World That Can't Stop Talking"

Please read this. First off, it will make you feel better about yourself and realise that there are many people like you. It also addresses the "Asian introvert living in outspoken America" cultural issue.

To meet people, you need to change your environment. Put yourself in situations where you are forced to interact. Groups or meetups are a great place to get started. It depends on your interests but something active like a sport or dancing will generally help you form better bonds.

Will it happen right away? No, but keep going on a weekly basis and become a regular. You'll find that friendships will happen.

To initiate friendships from these situations, you need to move the relationship to another setting. If you only see the person at the meetup, it's more of an acquaintance.

If you get along with someone you can say something like "Hey, I'm thinking of seeing that new movie this weekend. You want to come along?"

The envy you feel when you see groups is a good thing. It means you want to move in that direction.