I met my current fiance by helping Chinese students, meeting her at a dance ball, and then meeting her again by helping her neighbour.
I met my ex by walking a friend home, we met, and she and that friend conspired to bring me to lunch, which I agreed to.
I met another by walking into the university observatory and chatting to her about astrophysics and then fantasy books.
I met the ex before by joining the choir and she kept staring at me.
I met the one before that by walking to class and chatting to her as we were going the same way and I was lost.
I do not remember the ones before then. Generally it's a case of be nice, be around and be funny; people will take notice. Make sure you're well dressed and enjoy yourself. Finally, no one will find you if you stay in your room.
Regarding dates, it is generally "Hey, I want to go do this thing, want to come with me?" I've gone to parks, cinemas, museums, we go to other towns nearby, we try different restuarants, we look around book shops together, I go with her to get a present for her sister, she politely waits for me to finish staring at 40k in GW, and I would cook for her whenever I could because she can't cook for herself.