Making friends at work – politeness vs genuine interest?

I’m in my early 20s and probably just about have a handful of friends. This isn’t a problem in itself as I’ve always been happy with a small group of friends, but I don’t really make new ones (or know how to) so my concern is about what may happen when friends drift further away as many tend to do as we all get older.

I think I’m a pretty normal person, definitely more introverted than extroverted but not to any kind of extreme extent (e.g. I enjoy going clubbing and have been into all of that since way too young). I don’t have trouble being social at work and my job relies to an extent on having social skills as I’m regularly talking to and meeting new people professionally. I’ve also almost always had girlfriends so I’m fairly sure I don’t have any kind of massive red flags that would cause people to want to avoid me.

I’m beginning to think at least some of my future friends will be people I meet at work especially due to the amount of time spent at work in this industry. As I said, I get on with colleagues quite well, some I’m closer with than others, but I have no idea where the line is drawn between people being friendly in a polite professional way and where there is the opportunity for genuine friendships to be formed. Even if I did know where this line was, I would have no idea how to go about 1) instigating this friendship 2) transferring this relationship to outside of work and 3) maintaining it should one or both of us move on to another company.

Any advice?