Research, like construction, is done post by post in the same manner. You decide a tech to start researching and you advance by adding 1 to the count with every post. Simple as can be. You do not advance your research progress based off of anyone's posts except for your own except in very specific circumstances (such as the below mentioned joint research). Special projects may present themselves on rare occasion and technologies may be shared assuming that the receiving party has the prerequisites for the technology in question.
The guideline for navigation of the tech tree, deciding starting techs, and planning for research is described on the Tech Guide full page.
Reverse Engineering Edit
Reverse engineering technology requires the salvage of technology from a battlefield or wreckage, and the example of technology used in the reverse engineering project is destroyed upon completion. Reverse engineering takes half the time to research, if prerequisites are not met then instead you may research a prerequisite in half the time.
Joint Research Projects Edit
Joint research projects work similarly to standard research, however, posts by both parties involved contribute to the same pool of posts for the tech, sharing the workload between the two posters. This is not the same as tech sharing, you may not do a joint research project on something either party already has.
Technology Sharing Edit
Technology sharing works similarly to reverse engineering, it takes half the time to research as the project normally would take, and prerequisites must still be researched prior to the intended technology.