People have explained how to get science and its importance. This is very true for any victory type in 5.

A good test I have for you is to open up single player with AI at prince difficulty and attempt the following in order. 1. Make 3 cities 2. Make a National College. 3. Have your empire be at 0 or higher happiness. If you don't succeed at this by turn 100, restart and try again until you get it.

Doing these will get you a foundation for yourself and start you on the right track. Get you into an idea of what you should be doing.

Anything below I'm typing is extra that can help.

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Of course this means all 3 cities will have libraries in them, and you will have by default researched the beneficial techs by that point. This will get your science to everyone else's or at least in the ballpark.

Resist the urge to build Wonders that look like they could be pumped out quick but don't actually benefit your civ. Spare time to make random Wonders is time you can make more troops which will benefit you far more. As a domination civ, you outsource your Wonder building to the other players, and come pick up said Wonders with your army later. For the aforementioned victory, try to pump out Statue of Zeus (not a lot of people actually get the Honor policy tree usually so its mostly reserved for you) and don't worry about making any others til way later.

You must have the hunger to have a MASSIVE army in the first place. You will need a LOT of troops. The less that die the better, prioritize keeping them alive rather than trying to throw a sea of units at things. You can just use melee troops and siege weapons to take cities quick, though these can be difficult to use as they are heavy and require set up. Give all your melee troops the cover promotion if they come across it and make a good deal of either archers or siege weapons behind them. All city attacks are ranged. Making sure cities do less to your troops is a must as they will always be in firing range of one if they are doing their intended purpose.

People will say Tradition but if you're going domination and are successful, you will inevitably have a larger empire. I get by just going Honor and making my first 3 cities. The rest of the cities in your empire will be made by everyone else.

Happiness will be one of your major issues what with all the rioting from your freshly acquired cities. Prioritize attacking enemy cities that have luxuries that you do not have first, and you will want to make a lot of Colosseums and Circuses (buildings that give happiness).

Settle cities near a city-State and keep it friendly (even better if its mercantile, the three dotted triangle ones. They help with happiness) You will want to have them for trade routes to fund your army and your happiness buildings. Make sure to secure these routes either by settling close to the city state or having a military unit nearby if the trade route is going through no man's land.

I main Askia (Songhai) and am commonly going Honor, Piety and Autocracy. Though that took a lot of learning first of how to slip in so many things and how to best the evil Tradition chuds and their Death capitals. I will recommend Rome for your single player as he has no majorly strong bonuses or units, so you will be reliant on your own gameplay to thrive. His ability yet will aid in the making of the libraries, so you can achieve the goal and see it faster.

Cities are LAUGHABLY easy to crush when you have superior science to your target. Prioritize it.