Cities

You have a ticket to your nearest city in your items, plus you can be invited to other cities and "visit" their city center in order to create an entry in your travel list.  You may have lots of cities in your list, and you may visit lots of cities - and there are many reasons to do so.  Traveling to a city does not make you a member of that city.

You can only join one city at a time, but you can always choose to "leave" a city and "join" another.  You join a city by building a house there.

In the city of which you are a member you may have oil wells, crystal huts, research labs, armories, etc. and you can convert crude oil to refined oil (necessary for entering dungeons) if that city has a refinery.

Oil wells (crude oil):
Every city has oil wells.  If they look like grass covered oily holes, they are unclaimed.  You may claim it using wood (if you are a member of the city).  Once you have claimed a well, click on it and tell it to create a golem.  Then click on the golem and tell it to gather crude oil.  The size of the well (small, medium, large) will determine how many golems can work it simultaneously.  At any time you can click your well and collect the oil the golems have produced.  If you don't collect for a while the well will become full and the golems will stop producing.  You can increase the capacity of your well if you have researched that option in a research lab (also built in citites).

Crystal (huts):
If you see a crystal patch you may build a crystal hut next to it.  Each patch can have up to 3 huts, though only one per player.  You may personally have multiple huts but they need to be on separate crystal patches.  A patch with more than one hut will permit additional golems to work each hut, so there is an advantage to building next to a patch that already has a hut or two.  You cannot create golems here, but must create them at an oil well and walk them over to your hut before telling them to gather crystal.

Refined oil:
You refine oil at an oil refinery at any city that has one.  It costs one crude and one food to make one refine oil.  Dungeons cost 20 refined oil to enter (10 if you're a platinum member).

Golems:
Golems are stupid creatures, easily lost.  They can jump with you to your kingdom or your war camp or your city, but otherwise they have to follow behind you and if you jump more than one flag at a time (or fail to wait before jumping again) they'll be left behind.  You can always go back to get them if you know where you lost them, or use a compass to find them and travel to them (or call them to you under certain circumstances) but it's best to just move slowly and carefully in small steps.
Golems can be used to gather oil or crystal, or be trained as offensive minions using an armory or other war building.  You can have up to 50 golems, but you'll need to research the additional golem capacity in your research lab and pay for the upgrades.
Archers and swordsmen can also be fused.  If you fuse two units (or up to five) it still counts as two (or up to 5) but they all fight as one unit.  They have the full HP of all units together, and the full fighting strength, but they can only hit one thing at a time.  The biggest advantage, besides not having a mob of critters around you, is the increased HP.  Having an archer killed means training another one (which takes 22 hours).  Fused golems are harder to kill.
You can also garrison your trained golems in your city garrisons.  When killed, they automatically regenerate in 20 minutes.