1) Wait for Energy
2) Buy/Use Energy items from the store
3) Complete side cases for Energy Items
4) Request Energy items from your friends
5) Complete a cooperative investigation with your Friends to gain energy
Last but not least, Level up gives you full energy. Anyone reading this, did I miss anything?
For #4, on your top navigation panel (where it shows how much energy you have), click the plus sign for the energy box and you will have the option to "request" energy from friends. Obviously, the more friends you have, the more will send you your requested item. The energy shows up as "coffees" worth 2 energy points and they reside in your inventory, which is the red box on your bottom navigation panel.
#5 means visit your friends and find 10 items within the 60-second time limit. You will receive 3 energy and a supply that corresponds to the friend's specialty. For example, if you visit a friend who is a body specialist and find all 10 items within the 60-second time limit, you will receive 3 energy and a gauze.
Also, when you send gifts to friends each day (the first thing that pops up when you open the game) and they accept, they have the option to "send a gift to say thanks." If you're sending coffees, they'll send coffees back.