For all the technical planning that goes into moving, whether across town or across the continent, the emotional aspect is not often talked about. When we moved I was so wrapped up in selling my house, arranging a moving truck, and finding a place to stay it really didn't occur to me just how much our family dynamic would change. Thankfully modern technology has made it pretty easy to keep in touch.
Of course we can always pick up the phone. My mom and my daughter enjoy a weekly video chat. Sometimes the phone gets passed off to me for transport so they can play hide and seek over Google Hangouts!
Grandparents enjoy getting packages filled with artwork and homemade gifts periodically. They return the favor with stickers and special treats. We also create homemade newsletters describing fun activities, milestones, and creative stories for out of state family.
My daughter has her own family phone book. It's a photo album with each page dedicated to a long distance relative. It contains a photo, short story describing who the person is, and contact information. This helps her stay in touch, add stories, and recognize family when we visit!
Social media is an obvious outlet. For those who prefer more privacy than Facebook offers but more variety than Instagram, consider a virtual baby book app like Moment Garden. They're only accessible by invitation allowing families to share pictures, videos, and short stories securely.
Keeping in touch with family after moving is very do-able thanks to technology and a few creative ideas. The quality of a relationship is not measured by miles apart, but by the love and effort put into staying in touch.