Training

In eRepublik you can train once a day to gain strength. You can find your training ground if you click on "My Places" and then select "Training Grounds". When the window opens you can select on which buildings you'd like to train by clicking on the empty squares and then pressing train. 

For every training you complete your strength will increase for at least 5 (depending on the training buildings you've selected), and you will also get 2 experience points (exp). Every time you gain 250 strength you will also receive a Super Soldier medal and a reward of 5 gold. More strength also means more damage in battles so it's essential that you complete your daily training in order to advance.By working and training you also lose health. You lose 10 energy for every training or work you complete. You can restore that by eating food which you can either buy on the Market under the food section or eat the one already in your storage.

Upgrading
Training grounds work similar to companies. You can either build them or upgrade them. My advice is to wait until the discounts to upgrade so you won't have to pay the full price. By upgrading them you will be able to gain more strength when training on the upgraded buildings.