I presume you mean to ask me how people communicated over long distances, because otherwise the answer would simply be ‘they talked to each other, just as they do today’. I’ll give you the benefit of the doubt, but please be more specific in future! (Kidding!)
OK, so 100 years ago, in 1914, the telephone was still in its infancy, relatively speaking. 99 years ago, Thomas Watson made the first coast-to-coast phone call in America, so that should give you some idea of where the telephone was, development wise.
However, the invention had been patented since 1876 and 1877 had seen the first long-distance phone call placed. But by and large, telephones were not an overly common part of people’s lives the way they are now.
More common was the telegraph, which had been knocking around for a while by then. People in official positions tended to use that, but it wouldn’t have been a fixture of regular people’s houses.
Far more common than telephone or telegraph was the postal service. In 1914, if you wanted to contact a friend, relative, or loved one, you wrote to them. The working classes were better educated than at any other time in history (up to that point) and literacy was improving (although it certainly wasn’t at the near-ubiquitous level of today). Letters took a long time to arrive by today’s standards, so they tended to be longer and more absorbing than, say, a Facebook chat is today. In fact, intellectuals, authors and politicians would often engage themselves in long-winded and exhaustive intellectual contests via thorough, essay-length correspondences.
Another option would have been to speak via mutual acquaintances. Literature of the period frequently involves friends using a mutual friend in order to carry on a long-distance discussion and it is my understanding that this was quite a common practice. Interestingly, this may very well have shaped the development of certain customs in society (such as ‘good manners’ vs. ‘bad manners’ regarding correspondence etiquette). With our communication methods of today being so vastly different, it remains to be seen how our society will come to reflect this.