Scenario setups usually don't allow you to expand freely since your enemies are quite close to you.

Sell city improvements that are not so useful. You get instant cash and reduce your burden of maintainance. Definitely sell courthouse of your capital city, harbor/port facility/coastal fortress in your inland cities, cathedrals when you have MC, and power plants/hydro plants when you have HD(those are designer's mistakes). Sometimes you can also sell universities, libraries, and granaries for more useful things like airports.

The first and second in power (supreme and mighty) usually don't like each other. If you are not one of the two, take the advantage of their conflict to buy some time(AI civs may ally with you when they are in war with other civs); if you are supreme or mighty, extort the small civs for contribution and ask them to declare war on the other superpower.

Some scenarios have super strong barb units. Bribe them and use them to attack your enemies.

Research should concentrate on war techs (the ones can bring you new types of units).

Build/occupy those wonders which allow you to sell city improvements. If you have a lot of granaries, build pyramids then sell them; a lot of cathedrals, build MC; a lot of plants, build HD; a lot of police stations, build WS.

Study the AI units and know their AI values. Some units are used as attacking forces although their defending factors are high. If an AI civ has a lot of such units, park a good defense unit outside the AI cities and the AI will use its defense forces to attack you -- when they lose you have less trouble taking the cities.