As far as I can tell, there is no UFOpedia anywhere in the game. In stead, the information is sprinkled around the game, to more or less appropriate places.
Research and Engineering screens house the largest collections of data.
The Research Archives have all the research results in them and have a rather detailed description of most things that go though your Research Lab. However, no actual stats can be found here.
The Build/Buy Items menu has a wealth of information on everything you can build yourself. Besides the flavor texts obviously visible, actual stats for an item (where appropriate) can be found by pressing the question mark button on in the lower left corner.
Rest of the information is more out of the way.
More item stats can be found via the Solider Layout screen, by pressing the icon on the lower left corner of the item's picture, be that in the Inventory or the Locker. This is also the only way to see stats on equipment you don't build yourself, like basic weapons and granades.
Clicking on any ship in the Hangar Ship List gives you acces to the stats on your available ship weapons, including Avalance Missles that you can't find in the Engineering. Click either Weapon Info or Edit Layout. You can also find some info on the ships themselves, altough they don't have any accurate stats.
Gray Market in the Situation Room gives you a bit more flavor text on some items.
The rest, including complete lists of accurate alien abilities, can be found in combat by targeting an alien and clicking More Info on the thing that shows your chanses of hitting it.
You'll also find more info on your own soliders' abilities by clicking the Solider Info button in lower left corner, next to the turn end button. Or, just by hitting F1.