Point One. You're the Union, man. You have more money, more resources, and more time than the South will ever have. Fill the Shipping Box with transports and let even more money role in. First, build! Second, build some more. Third, buil... well, you get the idea

.
Annie, Get You Gunnnnn-boats. Build them, put them in stacks of 4 boats to block crossings on all the river locations you don't want him to cross, which is nearly everywhere. When you get a chance (enough conscripts and money), build a transport for every other blocking gunboat stack. Gunboat stacks can draw supplies from neighboring transports in fair weather.
Have reserves stacks. When one stack on patrol is getting close to the end of its supplies or has lost some cohesion, send a reserve stack to take its place and send the tired, hungry patrol back to port from R&R. You should be doing every couple of turns, if not more often than that.
Put your ironclads at the far end of your gunboats, toward from where the enemy is coming--down the Mississippi. These are your Spartans, your Phalanx, your spear point. They must be in OP so that an enemy fleet trying to sneak up river will get run through. If they are in DP and the enemy fleet is in DP, they will simply sail on by and wave friendly. Ideally, you should have two ironclad fleets, because being in OP, they lose cohesion quickly. Cycle them through about every 2 or three turns. DON'T let their cohesion drop below 75% of full, or else they will do poorly in battle.
Keeping the South blocked at the major rivers reduces the forces you need to keep in reserve behind those rivers. If he does manage to get across, use rail to oppose him quickly. Deny him supplies and don't let him escape across the river. Once you've gotten him cornered, he's a dead duck.
If Davis has sent hist huge killer stack out to smack you around, get the heck out of the way. He can only have his killer stack in one place at a time, which leaves 10 others weakly held. Take advantage of that.
If you get your troops out of the way until you can concentrate your forces, what's the worst he can do? So he sits in Louisville, or even Saint Louis, or even Indianapolis or Cincinnati; so what? The further he is away from the the Deep South, the more vulnerable his supply lines are.
Once you've pulled your defenses together, let him hit you a few time. Defending with a good force on good terrain is the best way to bleed an enemy; and let him
bleed 
. oops, wrong era
If you did a good job of cutting his supplies, once you start really fighting, he will be in trouble trying to get more supplies. Then it's time for you to do this:

. Hound him, dog him, don't let up for as long as you can, because now he's weaker that he was and only getting weaker all the time.
Point Two. Know your best commanders, and know them well. Protegee them. Give them the best troops and lots of them. Let them fight weaker forces to gain experience and get promoted. Grant, Sherman, Lyon, and Kearney are your first Protegees. Use them well. Grant in charge of a good army is unstoppable. Sherman almost equally as deadly.
In '62 you get a couple of 4-1-1 leaders. These are good as small army commanders for places line West Virginia and Missouri-Arkansas. If you give them two good divisions each, they are very effective. They are active most of the time, and are equal to a small army or average corps.
Don't forget to take New Orleans as soon as you can. In the winter of 61-62, while Virginia is settling down under the poor weather, you can pull a couple of divisions from the AoP and sail them down to NO, take it quickly and leave one division to garrison. If you have enough forces, you can leave more than one division as a force to strike out into neighboring areas, Baton Rouge for example. This forces the South to pull troops from the front to guard against you riding rough-shod over Mississippi and Louisiana.
Get these tips down and practiced and you'll be well on he way to putting Davis into a dress
