Research available to be spent on Technologies is displayed under the Experience Bar, next to the book icon. Mousing over the icon displays the Research rate in the current Dungeon. Research accumulates at 6 research, per level 1 Warlock, per hour (+20% per Warlock level past 1). Then, it is multiplied by any Research modifiers. You can see the items and upgrades that provide Research modifiers in the Library article.