Which watch model? Where and when exactly do you see the warning about full memory? Is it on the watch at a specific operation, or in Garmin Express? Is it when you try to install a Connect IQ app? Or when you are trying to update the firmware? Or when saving a new activity? There are different sections of memory, and the solutions may differ, depending on the exact circumstances.
Generally, when using Garmin Express, and there is low free storage on the watch, Express suggests to clean up the Activity folder. You can do it also manually yourself. You can connect the watch to a PC (or to a Mac with an OpenMTP driver), and then you can clean up the following folders:
//GARMIN/Activity/ - all files
//GARMIN/RemoteSW/ - all files
//GARMIN/Debug/ - all files
//GARMIN/Courses/ - remove unneeded courses
//GARMIN/Workouts/ - remove unneeded workouts
//GARMIN/Text/ (if exists) - remove all unneeded languages
//GARMIN/gmap*.img
On some models you can also delete music, maps, and possibly other unneeded content. If you have problems installing a new Connect IQ app, then remove some other Connect IQ apps.
