I don't know about Japan specifically, but I live in South Korea and I understand the concept is similar.
We got phones when we got here. I have 300min/300text/unlimited data iPhone for around $70/month for a two year contract. There's a number I can call in order to call to the States. It uses my minutes exactly the same as if I were calling domestically. When my husband was over here without me, he paid an extra $25/month (or so) for a US number that I could use to call him.
Another option is Skype (or other apps). If she gets a smart phone, she can use the 3G for internet and use her phone as a headset.
Most days, I simply use Google Chat to talk with my family back home. The internet is excellent here, so oftentimes the connection is better that way anyways, and it's more like talking face-to-face. It's definitely better with my 2 year old son, because his grandparents can see him.
It works better for me to contact MY grandparents over the phone though, because the internet is a bit elusive for them.
When I studied abroad, the school was very helpful in setting people up with the information they needed. I didn't have a phone while I was there (I simply prefer the internet) but all of my roommates did. She may even be able to arrange to simply complete the contract that someone else in a similar situation has already started.
I really wouldn't worry about getting her one until she gets to Japan, because Japan also operates on a different frequency than most other places, so it's possible that whatever she brings over won't work at all.