If you both have apple devices, then iMessage or Facetime are the obvious choices. Since you are asking the question, I'm assuming you don't have apple devices so this isn't an option. But don't worry, there are other options out there.
If you don't both have apple devices, then I recommend Text Free. It will assign a phone number to the tablet. Then she can text you at your phone number through the app, and you can text her using the phone number that it has assigned - it will look like a regular text on your end and the text will show up in the app on her end. Texts are all free through the app (if you are ok with ads, you can get rid of the ads if you pay for the app). It does work as a regular phone number - she can call you using the app and you can call her, but it charges per minute for calls so you probably want to limit that to emergencies.
If you want to be able to call and see each other to talk, not just text, then the most popular choice is Skype. This has more functionality than TextFree because the video calls are free when you are both on WiFi. The difference is that you both have to use the app to communicate, where in TextFree, only she needs the app, you use your regular text function that is already on your phone.