Intro
Alright, so you have a good understanding of the game but need more information. You came to the right article.
Selecting multiple unit groups
Hold both left and right buttons while moving the mouse to select troops from an entire area.
Understanding the movement penalty
Movement into another player's lands is around half the speed of that of moving through your own. If playing with an ally, you may wish to coordinate attacks to provide monochromatic routes for both player's armies.
Never leave artillery on the front line
Keep infantry and tanks between your artillery or railguns and the enemy. If the expensive artillery is stacked with the cheap melee troops they may be destroyed even if you win the battle.
When in doubt bombard before moving in
If you believe a province has a high level fortress, bombard it before moving in. However, if the enemy keeps a single army in the high level fortress, you can take the fortress relatively intact with a large stack of ground troops.
Knowing were to place railguns
Keep railguns between provinces to make it harder for your foes to do a wild stampede and take out your railguns.
Make sure you don't lose your capital
If you are able to defend your capital , do so. Losing it means losing half your money!!!
Guard artillery with railguns or bombers if possible
If you want to win keep your artillery within range of your own bombers or railguns so you can hit the foes with both.
Spy on your foes
Place intellence and military sabotage spies on your foes. Destroy his factories and his railways.
Submarines
A submarine can be used to place a enemy battleship into hand-to-hand combat. While this is going on you can bombard the enemy battleship, with one of your battleships or light cruisers.
Make it so they can't retreat
Use a division or battlegroup to get the enemy's troops into hand-to-hand combat and bombard those enemy troops with railgun(s) and artillery.
If the enemy capital is an easy target annex it
Sack the enemy capital if it will not cause too many losses. You will receive much of their money. However, if you are sweeping up an entire AI country, you may wish to save the capital for last. When you take the capital each territory previously owned by that country will get a 10% morale bonus instantly. A good human player will spend his money to sabotage you while you are doing this, so grab his capital quickly.