In terms of serious/marriage relationships I've been only in one (and the guy is my DH now). However, I've been approached gazillion of times, some even pretended to be my friends and some didn't even care I'm already taken. Anyway, if you are interested in how it's like to date Japanese guys (or if you are already dating and just want to "compare notes" lol), read on:
Even though many forums and blogs will tell you that "Japanese guys are shy", I think it really, really, really depends on the person. Like, I wouldn't even generalize here. I've had guys asking me out on the first meeting and some even before meeting in-person! Some kept pursuing me even after hearing I'm not single, and some even went through the trouble of pretending to be my friends/students/clients so that it will be "harder" for me to reject(??)
Frankly, "do you have a boyfriend?" would probably be one of their first questions, whether you meet in a bar,club,school,work,wedding...probably even funeral!
Now, I'm sure some guys are shy, but I think the percentage is rather similar to any other foreign country.
My own DH is a countryside-boy, but he too wasn't shy at all and asked me for a relationship pretty quickly...
PUBLIC DISPLAY OF EMOTIONS:
Here I have to agree that the percentage of Japanese couples displaying public emotions (kissing, touching butts, making out in parks, etc.) is wayyyy smaller than in the foreign countries I've been to, but it does exist.
First of all, what I noticed is that holding hands in public is largely acceptable. Secondly, my own DH doesn't mind kissing
SAYING "I LOVE YOU":
DH and I say "I love you" every day and several times a day...but I realized that it's because we communicate in English. Saying "I love you" in Japanese doesn't sound natural...like in terms of the language itself, not because Japanese people don't want to say it. Err my point is that if you want your J-guy to say "I love you" talk to him in English :D
HOW TO MEET JAPANESE MEN/HOW TO GET A J-BF:
In my case, I met my DH because we were colleagues, but more common ways to meet are:
1) Online. So many guys openly state they are seeking for a girlfriend/marriage partner. And from my experience, even when you go to non-dating website and join FB culture exchange groups/hobby groups, where guys state that they are only looking for "culture exchange/language exchange/friends" most likely they will try to pick up on you anyway.
2) Bars/Clubs/universities/your own workplace in Japan. Obvious choice, isn't it? lol
3) Become a language teacher. I didn't know for sure until recently (although I was starting to get suspicious) but, it's actually a famous way "to get a girlfriend" among Japanese men. Like, it's actually written on the net when they google "I want a foreign girlfriend" or something like that.
So, big disappointment if you are actually hoping to get "real students", but a great way to meet men who actually have a stable job with nice income.
4) Basically, any-and I mean it-ANY event/place! Japanese guys wouldn't approach you in a cafe and would unlikely to start a conversation on the train, but other than that, any place I went to and any event I've attended to had at least several J-guys actively hunting for a girlfriend.
Good luck :)