At lower levels, the root of technology lag is not enough gold per turn (gpt). Even at self research (you research all the techs yourself) you should be able to launch a space ship well before 1800AD (map quality may vary).
Even if you make the mistake of research top to bottom rather than left to right and don't trade a single thing, at warlord you should be able to outpace the AI.
So,
first - when you research, climb up the tree. Up is left to right, not bottom to top. The faster you go up the tree, the more the techs are worth in a trade.
Second - trade.

If the AI has something you need, give him something you've got. Try to trade a new tech to every civ you know
during the same turn. If you don't, the first AI you trade with will spread the tech around and you get zip. Eventually you will be so far ahead the AI will not have much worth trading except gold, gpt, luxuries and resources. But those are nice too.
Third - Science Slider. Move the science slider from 0%-100% and you can see the range.

Make sure to play with the slider every few turns (or every turn if you are obsessive like me), but at the very least play with it on every turn for the last 4 turns. Often you can adjust the scale and get the tech in the same number of turns but also net some gold. Fail to do this and you lose out on the gold.
Use tech trade to build up your treasury and gpt so you can 'deficit spend' on research. If you have 1000 gold in your treasury, it doesn't matter if you are researching Replaceable Parts in 4 turns at -58 gpt. Research the tech and then use it to rob the AI blind. Make them pay for your research.
Forth - gold per turn (gpt). Research is really all about how much gold you can produce per turn. That means you need cities - if you don't have some cities at your borders that are 95% corrupt, then you did not expand fast enough. These cities need to be big - the bigger the better so long as you can keep them happy. Working citizens make lots of gold. But only if they are working on improved tiles. So make enough workers (recommend about 1.5 per city) to improve all your land. More Cities=More Citizens=More Gold=Research.
**Danger** Almost everything you build in a city cost gpt to maintain.

Check your maintenance costs on the F1 screen. All those colloseums, barracks, temples, banks, and libraries cost money to upkeep.
Only build what you need in the city. Everything else is wasting gpt. Same for a large military - check your unit support on teh F1 screen. Make sure it is 0gpt or a reasonable amount (in republic/etc.). Of course, make sure you have enough military to handle any conflict that might arise.
Fifth - Even more gold. So you've got big cities and lots of citizens but it still takes a long time to research everything? What you really need is something to multiply all that gold. Solution? Libraries, Universitys, Labs. If you want to bury the AI in research, build them. Marketplaces are good because multiply luxury happiness. Banks and Stock Markets - maybe if you are not running research at 100%. Consider that carefully because you'll be paying gpt for maintenance and that defeats the purpose. As previously mentioned, take a hard look at each building you are going to construct and make sure it adds something you need. At warlord you can get away with quite a lot, but that only makes the temptation to build all the stronger. I'm a natural builder, so I understand that urge.
Sixith - Even MORE gold. Governments. You can bury the AI with any government at Warlord (but please get out of Despotism as soon as possible anyway

). You can go Monarchy or Republic and you'll be just fine. Most players prefer Republic because it gives an extra gold for every tile worked that is already producing gold. That means +gpt. With that said, Monarchy is a easier government for new players to deal with, in my experience.
Seventh - Science Farms - won't go into that here unless you want to know more, but corrupt cities should be used to hire scientist - as many as the city will support.
Good luck!