Well, that's a question with a lot in it. Some very basic tips:
1. Put your best generals in charge. A mid-high strat rating is key, especially for army command. Defense and Offense stats are also pretty dang important. A General like Big Mac, Butler, etc with low stats across the board will actually make the corps commanders under him worse. Depending on the setting you have, an inactive general could suffer 35% loss of effectiveness. Higher strat rating generals are less likely to go inactive.
2. Avoid Command Penalty: It's better to have a leaner well led stack than one that's so large your general(s) can't effectively lead them. General Command Penalty can be your opponent's greatest general, don't let him affect you if at all possible. 1*s provide 2 command points; 2*s provide 4 command points; 3*s provide 6 command points. Up to 4 generals can provide command points to a stack, after that there's no gain. So 4 one star generals will provide 8 command points and 10 one stars will still only provide 8 command points. An army or corps stack will double your command points available, meaning you can put more men without suffering penalty. Support units like HQ, Balloons, and signal units can provide additional CP. Some generals have traits that raise or lower CP.
3. Attack with superiority of force: This period of warfare favored the defender and this game does a pretty good job of emulating this. Try to attain 3-1 odds when attacking. Try to avoid attacking heavily entrenched forces if at all possible. If it's feasible manuever around them. Take ground that your opponent can't let you have (sitting on his supply route for example) and let him attack you. If corps formations are available don't forget that adjacent corps or army stacks will support each other by marching to the sound of guns (MTSG). With MSTG, you might think you're sending 3-4 corps against a single enemy corps only to discover that two additional enemy corps supported the enemy target corps. Pay attention to things like weather, attacking over rivers, attacking in swamps, etc that can negatively impact your forces and plan accordingly. Sometimes it's best to just sit the weather out.
4. Force Composition: Cavalry are great for the pursuit phase of a battle and can help inflict lots of casualties but they suck going toe to toe against infantry. Cannon are a great way to soften up the enemy force before your infantry clashes with theirs. But having too much artillery could deprive you of the staying power in multiple engagements as you run out of infantry to hold the line. Infantry will be the biggest part of your force. Militia<Conscripts<Line Inf<Elite Inf. Try to stay away from the lower end of that spectrum if possible. Don't forget about units like sharpshooters or marines to help your units out.
5. Are you well rested and supplied? Tired troops will perform worse in battle. If you've marched a lot recently, let them rest for a turn or two and regain cohesion. Adequate supply is key. Keep at least 1 supply wagon with your stacks will let them fight longer and those wagons also give a combat bonus. Most troops will carry enough ammo for two battles and enough supplies for two turns. Don't get caught out of supply as you'll take huge penalties to your combat ability. Like I said, the importance of supply wagons cannot be overstated. I can't count how many times having supply wagons saved my bacon when I had to fight 3+ battles before I could resupply. Some people say you need 1 wagon unit per division. I usually follow that general rule of thumb out in Kentucky or points west were travel takes longer and depots are few and far between. In more developed areas, I might just keep 1-3 per corps. With my corps I'm rarely advancing all of them at once and can swap out wagons as needed.
This link was for AACW or the game this one's a direct descendant of, but lots of the information still applies. Just ignore the bit about the frontage rules for artillery not letting more than a max of four batteries fire.
http://www.ageod.net/aacwwiki/AACW_strategy_guide
