A lot of wonders (if not all of them?) show up as a visible model around the city in which they are constructing / constructed. So if you see a pyramid around a city, you know the the great pyramid is built there.
It takes some practice to know what wonder is what, and it's definitely a very crude way; requires scanning all cities for things that are sometimes very hard to notice. But it does work, I use this method often to know which wonder is being constructed by other civilizations, to avoid working on the same wonder.
Notice that all wonders have different "under construction" and "completed" models.
EDIT: I've found this wonderful page which attempts to catalog all wonders with screenshots of their "under construction" and "completed" models. Still incomplete, but useful nonetheless.
In general, I don't think there's any "optimal" strategy, everything is very situational - depends on the terrain, the units you have, the units your enemy has, specific promotions, etc. Still, I do have some methods I can share.
General Capturing
In general, to capture a city, the majority of the damage I inflict is from ranged attacks. I do use melee units, but mainly to protect the ranged ones and to soak damage from the city.
So, I move a few melee units to range 1 of the city but just let them fortify themselves there. Then I move ranged units - preferably siege units - to range 2 of the city (or more if it's later in the game and I have units with greater range), and pummel it until it drops to 1 HP, then a single melee unit can capture it.
Using melee units to attack the city is fine if you have enough of them - it certainly speeds the process - but since melee-ing a city is often costly it often leaves them too vulnerable to bombardments from the city or from other enemy units on the enemy's turn.
This is usually uniform across all ages, except that when flight is introduced I also use planes to damage the city, and also once I get range 3 units I try to soften the city as soon as possible, even before the core of my army gets there, just to make it quicker.
There's no rule for how many units you need. Sometimes just one is enough - a heavily promoted Rocket Artillery can bring a city down very quickly, then any single melee unit, even a weak one, can capture it. In the early game, when all you have is archers and warriors, you might need a few more - but almost always, when I think how many units I need to conquer a city, the decision is more about how many units the enemy has around the city, than about the city itself.
Finally, keep in mind promotions can sometimes play a large role. Bombers with the siege promotions are amazingly good against cities. Siege units with the logistics upgrade (two attacks per turn) can also bring them down quickly.
Capturing Cities on Small Islands
I understand you have a problem with this specific scenario. A few tips:
Use ships. It's true that early on ships don't do a lot of damage, but all you need is to be able to do more than 2-3 HP per turn and it adds up. If you can't reach that number, just get more ships. Range 3+ ships are especially useful, and the +1 range promotion isn't that difficult to get, especially if you level up on barbarians first. (and yes, even Triremes can get that promotion). Note: as of the Gods and Kings expansion, there are both melee ships and ranged ships, and you can capture cities with melee ships; I recommend this for small islands. Embarked units can defend themselves to some degree against ships, but they will still take heavy damage. The advice to do the majority of your damage with ranged units still stands, though.
Get the "amphibious" promotion for your melee units. It removes the penalty when attacking across rivers and when attacking when embarked, and this can really help for capturing coastal cities. Still, remember embarked units are very vulnerable - not only to other ships but to ranged attacks as well.
Once you get flight this becomes a different deal. Bombers can devastate cities and even fighters do a little damage, just make sure you have a nearby city or enough carriers. The AI does love its AA, though, I often find myself bombarding AA guns with ships and only them use the bombers. One final tip about flight - in my experience it's better to use fighters to air sweep and clear the way to bombers, than to use them to directly damage units.
Also, regarding your general problem with embarked units getting killed by barbarians - just make sure you escort them with real ships. Even Triremes have decent enough range and sight that they can effectively guard a few embarked units. Also remember the movement penalty of entering a tile adjacent to enemy units - that means a ship can effectively block the passage for other ships even when it only takes one tile in itself.
Best Answer
You'll get the ultimate end-game unit a few technologies earlier than the Giant Death Robots you're using now: Stealth Bombers. They have a range of 20, and a strength sufficient to damage any unit in the game. Better yet, each of their attacks is a melee attack, so they gain XP quickly. They'll take some damage every time they attack, but you never need to worry about them being destroyed: they're sitting pretty at least 10 hexes away from the action, so when they're low on health, have them rest for a few turns. Before too long, your stealth bombers will have both Logistics and Air Repair, attacking twice a turn and healing 20 HP at the end of the turn in their cozy cities far from the front lines.
Once you have a sufficient force of Stealth Bombers, the hardest part is marching your melee units fast enough to capture the enemy cities that your bombers are blowing to bits. Any enemy units will be obliterated by your flock of bombers as you walk your melee troops into city after city. Use your Giant Death Robots to take the cities; if you're having problems with enemy air units, try using Mobile SAMs, Paratroopers, or fast units like Mechanized Infantry or Modern Armor instead. (Mobile SAMs have defensive bonuses against air units, and Paratroopers can be air-dropped next to the city, so you only need to take one turn of bombardment before capturing the city.)
If you're being nuked, then try to pillage your enemy's uranium mines so they can't build any more nukes. Strip away the defending units with your bombers, then march in your troops to destroy the mines. Or simply capture the cities that have the mines, using your overwhelming might of your Stealth Bombers. Did I mention that Stealth Bombers are powerful?
(Side note: Stealth Bombers take about a dozen seconds to attack, which gets time-consuming once you have several of them. To speed up the process of attacking, switch to the Strategic Map first.)