After you have done your initial colonising, look at your planets and establish one specifically for research.

Best option is to pick the largest planet you have, although bonus tiles and research bonus obtained when first colonising should be taken into consideration (planetary bonuses can be seen under planet detail)

The planet should be close to a corner of a quadrant for maximum effectiveness.

Dont bother quickly developing the planet until you have your economy rocking,(in fact just build a few factories, a farm and a few stock markets, then fill out the remaider with research buildings but dont worry about buying them yet) but meantime research the research improvements and Xeno Ethics. Switch to neutral alignment and then research Neutral Learning Centres(NLC).

Once your economy is sufficiently healthy buy on credit a NLC every turn, including on the factory and stock market tiles at the end.

While you are buying the NLC's research the engine research tree, miniturization and life support. Then design the fastest constructor u can.

Next place a rally point near your research planet and switch all planets to build the fast constructors. When they arrive build 4 econ starbases in each quadrant so their influence overlaps the research planet...this is why having a planet in a corner of a quadrant is important... you can build in 4 quadrants for a total of 16 economic starbases that will give research bonuses to your research planet. Use the other constructors to add more modules to the starbases.

Also upgrade starbases over research resources (the most important resource IMHO, more valuable than a planet, better to build a constructor to grab one when the colony rush is on than build a colony ship)

Now research farming improvemnts then moral improvements then factory improvements, one level at a time, in that order. This should mean your planets wont need too much micromanaging if you have a reasonable planet build, ensuring farm upgrades are built before pop caps out, moral upgrades built before pop grows too big for them to whine, and factory upgrades which allow you to add more modules to your econ and resource starbases.

When the econ starbases are finished they will each give a 24% boost to research on the research planet!

When the planet is totally covered (leave one space) with NLC's research the research tree again, and build the Omega Research Centre on the research planet (50% research bonus on the planet its built on)

Now research the missile defence tree to the end and build the Hyper Computers trade good - build/purchase on another planet , 20% research bonus is empire wide.

Congradulations, you have won the game... the AI just doesnt know it yet. Flicking the focus onto research and putting research sliders well up means you will scythe through any research tree amazingly fast.

As I said best result is with a large planet in a corner of a quadrant, best is a PQ 26 planet which will upgrade to PQ 32 on switching to neutral alignment. The best planet I had doing this a few games ago was a PQ 26 which had a 49% PQ increase on colonisisation and upgraded to a massive PQ 64 on aligning to neutral.

With this planet, and research starbases I was able to generate over 12,000 research points which made quick work of the research. Typically a PQ32 will generate 6-8,000 research points if your have sliders up high for research.