Are you on King now? King is generally a good level to experiment and try various things to see what works for your style. I'd recommend just trying lots of different things with different civs - take different policies, beeline different techs, play peaceful, play conquest, play horizontal & vertical, etc. Eventually you will get a feel for things and your style will coalesce into some kind of actual strategy.
Now for some actually useful advice pertaining to your questions:
- it seems you have trouble keeping up techwise. Taking cities is only very difficult when you are outclassed, otherwise it's only somewhat difficult. If you are on even ground with your opponent, usually just a couple siege units and a few strong front-line units will do the job. it's very important though, to engage the enemy on neutral ground (i.e. not near their cities) and destroy their fighting force before attempting to invade their cities. You can live with the damage from cities, but when you are being assaulted by cities and units at the same time even poor AI will kill your units. Basically, beelining cities is no longer the strategy, kill the army first.
- the more dedicated you are to warfare, the easier it becomes. Taking cities is easy as pie if you have upgraded 3 siege units with extra range, logistics & indirect fire. It takes centuries of warfare (and careful protection of said units) to get there though. And you still have to be on the same level tech-wise as your opponent.
- with regards to tech, there are 3 ways to dominate the tech tree:
1) Out-expand everyone and rely on huge population & infrastructure
2) Stay small, build the NC early, then focus on gold and sign as many research agreements as possible
3) Focus on city-states and get to the scholasticism policy as soon as possible
These can be combined in different ways. Personally my favorite is #1, as that leads to the strongest overall economy. It's then easy to add bits of #2 and #3 if you go that route, which is not as true if you start small; it limits your options more. But on the other hand, certain maps & civs will make staying small more attractive, and in those cases, you definitely want to pursue either #2 or #3 (or both) aggressively.
Another general piece of advice that helped me a lot in moving from Prince to Emperor is just to remember to always sell your resources. Aggressively shop everything you've got at every opportunity. You can sell luxuries for 300, and Strategic resources for about 220 if the civ actually wants it. Open borders is even worth 50. Use this gold to buy settlers (best purchase most of the time) open up CS, sign RAs, or rush key buildings.
Diplomacy is another aspect you learn in this stage, and the more you understand it the better you will be. This ties in with the paragraph above as well - you will get better payoffs on your trades if you maintain "friendly" status.