Research actions fall into one of two categories: conventional research and superweapons. Conventional research is what it sounds like - you can invest dice into improving a technology found on the technology list, invent a new one entirely - fluff will likely have this be as you figuring out how to mass-produce an already existent scientist's project unless it's really out there like the Drillfiends were - or apply the technology to some other avenue. Science, basically. This does also apply to military doctrine and such, or designing a eugenics program - actually implementing it would be an infastructure action.
You may research any technology, whether it already exists or not, and I do mean anything. The Under-Empire is a giant melting pot of ideas, and for every idea there's a skaven out there that's had it at one point or another. However, more obscure ideas are harder to actualize than those with some grounding in known principles. What this means is that while it is perfectly possible to create an airplane or atom bomb, it will be far more expensive than if your techbase has concepts that will support it and ensure that you have something to build off of. As a general rule, the less technologies you have with a connection to whatever you intend to create, the more expensive it will be as more parts of it have to be created for the first time, with all the disastrous experimentation that implies.
Superweapons are entirely different. They represent those times when the skaven pour monumental amounts of lives, resources, and labor into one singular project that works wonders. Think of the Fellblade and the Morskittar Gun from canon End Times for examples. You can direct any clan to produce a superweapon (and giving at least a rough idea of what you want it to turn out as will help) or you can tell two or more to collaborate on one if you think that'll turn out well. Depending on the results, what you create may be able to be mass-produced with research, though that possibility diminishes the more dice are poured into the project. You can add dice to a superweapon over multiple turns, and assuming it isn't destroyed in combat you may use it and then upgrade it the following turn. Or you could make it a one-shot weapon like a giant bomb, your choice.
As with every other action, you may assign hero units to these actions at a rate of 1 per Authority. Some are better at certain types of research than others.