If you sacrifice a few siege units you shouldn't need to lose any other units.
Basic Technique to take over cities:
The army
Make sure you bring mixed arms, in order to counter any unit the enemy might have, spearman for mounted units, axemen against melee, swordsmen against cities. Bring several siege units per city you plan to capture. Build units with barracks, and +exp civics. Promote each unit for the opponent you are up against. +archery, +melee, city raider, etc. Promote some siege units with collateral and city bombardment or double collateral.
The attack
1. Move your units next to the city. If the enemy has siege units make sure you're stacks are not too big to avoid collateral damage.
2. Use your siege (with city bombard) to attack city defense to 0 or at least below 10%.
3. If you have enough siege units, you can continue, otherwise end turn.
4. Attack the city with your high collateral damage siege units. Yes, just barge right in. They will probably get slaughtered, but your goal is not to win but weaken multiple units.
That they die is a game balancing concept to avoid them being overpowered like civ 3. Basically what you are doing is swinging the odds in your favor. Going up against 10 units with 9 power might be impossible, but after 5-6 siege weapons they should be around 1-3 power and it's just a mob up.
5. Move in your land units, countering whatever is in the city where possible to help the odds more.
You should be able to take the city with minimal losses. Just heal up, replace siege units and continue