When considering how a soldier would write a personal letter from the trench today, it is necessary to consider the technical devices that are available to soldiers of the 21st Century. During World War I, the technology available to soldiers in the trenches were pretty basic: a pencil and paper. Today, there are many more options available to soldiers.
Assuming that soldiers have access to a smartphone or electronic tablet, soldiers could record their experiences in a variety of ways. The most private, safest and efficient way to record letters would be through emails. Soldiers could either email their loved ones about what they were up to, or they could set up an email account themselves to send messages to. If they chose the latter choice, they could open the emails at a later time to recall the events of the times they had in the trenches.
There are also online journals like Penzu or Journalate that could be used to record their feelings and actions during the times they spent at war. The online journals could be shared with others at a later time, or could remain private. Social media sites are not permitted to be used in combat zones, but that barely limits fast and efficient communication to loved ones. There are endless possibilities to use the latest technology to write personal letters home from the trenches.
A soldier may even choose a more personal touch and pen a letter to home in the same fashion men have been doing since the beginning of warfare. That is most likely what most soldiers prefer.