Several good tips have been offered, here are few more that might be a bit more esoteric:
1. Position your HE city well; not only do you want high

, but you also want it to be close to your likely targets. Within 3 moves of the sea is also good as you can then use naval shuttling to get to the front (even it is just ring around the coast). If you intend to have multiple

cities, try to weight them near the target.
2. Spies + mounted halves your walk time, at the price of making you extremely vulnerable to counterattack and eating into your

or specs.
3. Rushbuy. The multipliers for

are the first set to reach 100% in the game (aside from 5 mons or GP buildings); getting out to banking quick can allow you to have virtually no production cities so you tech fast and once you get a tech advantage after that (cannons are good), you just go 0% on all sliders and "build" faster than you can with hammers until assembly line. This requires that you snag the mids and commit early to heavy CE; not always wise. An alternative for early rushbuy (still requiring the mids) is to burn a few GM on trade missions and flip over for 5 turns and then rushbuy your units (you can queue load if you want more than 5 units per city you can devote to units for the iterim). This can be extremely useful for a GA or as a religious civ - slip into US/Vassal/Theo; rushbuy the newest wonder unit (phants maybe, perhaps maces or trebs, but definately good for Curis, cannons, and rifles).
4. Upgrade your units. Again it costs a pile'o'cash, but the fastest way to hit the AI with catas is to start with HA. If you manage to beeline Guilds before the AI hits feudalism this is extremely powerful, you can literally hit the turn after you get the tech. More commonly this is used to make CR rifles/grenades for a quick bash the LBsfest.
5. Resource denial. Hit using phantapult, camp their Fe before they get engineering and the age elephants lasts until gunpowder (or rifling if you have enough promos). This gets even more insane in the late game. 2 turns after getting nukes you can irradiate all the foreign U in the world and have a monopoly until they tech ecology. With oil you can have a tank advantage, but more importantly you can own the air. Each SAM enages only once and using carriers you can have enough fighters to never hit a full strength unit, ever. Camping on the enemy oil gives you ai supremacy for the long haul; after AdFLight Al functions similarly. Camping the oil and the U gives you naval supremacy for the long haul.
6. Don't attack at the AIs exterior. Landing your troops next to his main

and

cities (normally near his cap) allows you to nerf both his building rate and his tech rate.
7. Use diplomacy to isolate your target beforehand. AI-AI wars are great for depleting units and slowing research, but at the cost of GGs getting settled and making nasty defenders (CG III anything is damn annoying). Trade emabrgoes ruin AI-AI relations and help nerf the economy.
8. Privateers. Burn the seafood and either blockade while racking up caravel kills or play the navigation/circumnavigation game to burn and run; unhealthy low food AIs tech poorly. A properly managed Nav II/Circumnavigant privateer can play hit and run for a long time.
9. Spies, a dedicated EE has too many tricks to ennumerate. While most serious espionage comes out of research one way or another; if your research is EP then you can just go to town on your target.