Your research team will primarily be Dr Richard Tygen... just him. You'll need to recruit scientists when you can, either through mission rewards/rescues, home base hiring, or on rare occasion on the Black Market. Naturally, more scientists will reduce your research time. You can also build a laboratory or two to further speed things up.
Lastly, the black market will often have one or two items for sale in exchange for Intel: packs of detailed notes and schematics acquired from refugees and loose talkers that will reduce research time on some of the projects you have listed in your research backlog. The Black Market will update these available research credits monthly, at the same time as when you get the latest Spokesman's assessment and Supply Drop notification. The prices will drop if you've already made progress on that research project
Tygen himself is a former ADVENT researcher, who was basically shanghai-ed by ADVENT to run some of the earliest 'Gene Therapy' labs: this position let him see behind the scenes at the true nature of ADVENT's (and the Aliens) goals. Horrified, he eventually managed to contact Bradford and the remnants of XCOM in the Resistance. Occasionally, you may see him from behind, where you can see some massive scarring on the back of his neck: he managed to operate upon himself and tear out the implanted chip that ADVENT had put into his skull, showing his determination in opposing the alien forces.
Keep in mind that when you encounter new types of aliens/ADVENT in missions: you will only gather the corpses, and thus be able to do research on them, when the mission did not end with an Evac.
Also, be sure to Skullmine and Hack for Blacksite Facility leads, and gather any ADVENT/alien datapad drops: Tygen can research the leads for the Facilities (for a moderate Intel cost), which you'll then can assault without needing to first contact the local Resistance cell, and the datapads themselves for significant Intel rewards. If there are currently no active Facilities, the leads will go into storage; once a new Blacksite is put up by ADVENT (and is not 'discovered' right away anyways by being in a pre-contacted sector), they can be researched for the new sites.