I have 3 years of experience with this. The social stigma really makes it hard to act authentic and relaxed.
Not so proud moment:
The first time I approached a woman in a train I was in a suit at 6pm rush hour. Absolutely packed and she was right next to me. I said "Genki? Where you goin' to today?"
She literally turned her back on me and the entire train was silent. Most awkward 5 minutes-to-the-next-station of my life. Of course, the real irony, is I lost nothing from that interaction.
That burn helped me though. No arrest, No punch in the face from a J-dude...nothing, but silence and perceived judgment (all in my head) of an entire packed train at rush hour.
Proud moment (years later):
Girl I'm dating and me are at WOMB in Tokyo. Girls come up to us
GIRLS: "You two look so cute- how did you meet?
MY 'GIRLFRIEND': "He just came up to me on the Yamanote Line!"
GIRLS: Sugoi! How romantic!
My approach style:
I am NOT a master at this (some guys on Japan Lair are), but I'd say I have more experience than 99% of foreigners doing this.
"Excuse me" and then comment on whatever is in there hands, app, iPhone (
I used to literally say "is that the new iPhone"). Reactions differed like crazy, just like in a bar or club. Some blow outs, some numbers, and many instant dates.
All you can do is be confident (as Solong said), DON'T get physical, and be that "Quiet Train" style of gentle, soft spoken, but playful.
But my biggest advice? Understand you will, at some point, get horribly rejected and suffer through the RIDE OF SILENCE (like my first experience).
Feel free to PM me.