Training

Training performs three functions; training your soldiers as attack or defence specialists, or as spies or sentries, upgrading your covert skill level and upgrading your unit production

On the training tab, look to left left, and you will see a summary of your fighting force.
The categories of soldiers listed are "Attack Soldiers", "Defence Soldiers", "Untrained Soldiers", "Spies" and "Sentries". If you look to the right, you will see the options to train your soldiers.

The only soldiers you can train are your "Untrained Soldiers". When you gain soldiers they are always untrained. Untrained soldiers give 4 Defensive and Strike Action, and can use weapons with 4 times the strength (duplicate the strength by 4 - see the Strike and Defensive Action paragraph).

An important point to note is that Attack Specialists only participate in the attacks you make on others, and the Defensive Specialists only participate in the defence action when others attack others make on you. Untrained soldiers participate in both. Attack and Defence Specialist are only used in either Offence or Defence. As such, they only give extra Strike OR Defensive Action. Attack Specialists give 5 Strike Action, or duplicate a weapon's strength by 5, and Defence Specialists the same with Defensive Action.

You can also buy mercenaries either trained or untrained but thus is less cost effective than recruiting untrained soldiers and then training them
 
Sentries and Spies give a basic 1 to Spy or Sentry Rating, duplicated by the Spy level you have. This also heightens the effectiveness of your Spy or Sentry Tools. Remember that without Spies or Sentries, buying Spy or Sentry Tools has no effect.

The last option is retraining; this is basically undoing the training, thus bringing your trained soldiers back to untrained soldiers. Retrain itself doesn't cost anything but this shouldn't be used, as it is wasting your gold.

To train, make sure you have enough gold and untrained soldiers and put a number in the box under "Quantity" next to the type of training that you want

Upgrading Covert Skill

Scroll down to the tab "Upgrade Covert Skill" on the left and click the box beneath it.
Upgrading your spy level will duplicate your entire Covert Rating and Sentry Rating.

Upgrading Unit Production

Unit production is the number of untrained soldiers that you get each 24 hours. You can upgrade this to a higher level (and gain more soldiers each 24 hours) for gold. Scroll down for "Upgrade Unit Production" on the right. Click the box beneath it, and watch your Unit Production being doubled.