There are two ways to send a message to other geocachers. First, when looking at cache information after selecting one in a list you will see the cache owner's avatar (if they have one) at the bottom of the screen. Pressing it will open up the web browser and go to the geocaching.com website for messaging other users. It will preselect the user so all you need is to enter a message for them. You can also do the same for owners of a log by pressing the log when viewing a list of logs for a geocache.
Unfortunately, Groundspeak doesn't let 3rd party apps access messaging features directly like their official app does. So in the meantime, this is the next best way by going to their web site instead.