Vacation Mode can be accessed by going to the Options button on the menu on the left hand side of the screen. Once there, you can activate vacation mode (as long as there are no active fleets, research being done, or buildings/ships/defense being built) for a minimum of two days. You cannot be attacked or attack others during this period, and after 2 days you are presented with the option of deactivating the vacation mode. While vacation mode is activated, your resources will not accumulate, effectively freezing your account until you come back to use it.
This cannot be used to evade attacking fleets, for if an attack has already started and you go into vacation mode while the attack/incoming fleet is en route, it shall proceed as a normal attack/transport mission and you will not be able to move your fleet since it will be 48 hours till you can turn v-mode off.
If you find that you cannot activate Vacation Mode, make sure you have no incoming or outgoing fleets (check your Overview screen). Also make sure you have no ships, defenses, or structures building, and check that you are not conducting any research. Finally, if you still receive the message disallowing you from entering vacation mode, turn all your mines at all your planets to 0 Production Factor.
Vacation mode does not stop you being inactive; if you do not log in within 7 days, you risk the account being deleted after 35 days.
NOTE: After leaving Vacation Mode, all of the mine and energy levels are set to zero and must be manually reset on the Resources screen to return to full production.
Bug: There is a bug having to do with resources accumulated on planets since the last time that planet was accessed prior to activating v-mode. The resources are lost on entry into v-mode. To minimize these losses you should visit each of your planets with the Resources screen and hit the Calculate button, then check for incoming attacks and immediately activate v-mode.
I am not receiving base income while in Vacation Mode. Yes, my Storages have room.