Suggested Tactics
OFFENSIVE STRATEGIES
The main thing I can recommend here is not to make an assault on an enemy city without having all the necessary units nearby. For example, don't just send random assaults by single units. Instead send in several (say 5) assault units [Howitzers, Cannons, etc.], followed by a couple defensive units to hold onto the city after you take it. Also, don't try to take an entire continent at once, unless you have nuclear weapon and they don't. Take it a city at a time, with a few cease fires along the way, if you need to get your troops organized for more victories. But, if you do have nuclear weapons, just build a dozen nuclear missiles and twice as many engineers to get rid of the pollution, along with a comparable number of supporting ground troops. Just Nuke all their cities, and on the same turn, just walk in with your ground troops and begin cleaning up after the previous inhabitants.
CITY DEFENSE
The Main thing that seems to come back and bite you is to leave a city undefended, no matter how deep in your territory. A computer unit that you just happen to be at war with usually finds and conquers the city. Of course you just come and take it back, but you've lost all of your city improvements! So what I do to deal with this problem is to try to keep at least 2 units, (more if close to an enemy empire) one of which is defensive, [phalanx, musketeer, or rifleman] and an attacker. You can strike first, in case you see an imposing attack coming. Another good idea is to build fortresses atop hills or mountains and fortify a military unit so you can have a better chance of seeing an immanent attack approaching. Plus it'll help keep other empires' units from running circles around your cities, hurting production. Plus, and I can't stress this enough, you will need to build the City Walls improvement to increase defensive capabilities 50% and any other defensive improvements available. [Coastal Battery, SAM Missile Battery, etc.] Also, after you and a formidable enemy have discovered flight, fortify a Fighter Unit inside your most vulnerable cities to defend against Bombers when the enemy finally gets Advanced Flight.