To build or upgrade an infrastructure, you must select it in your Academy. You will then see what the current level of the infrastructure gives you (or the level 1 if it is not built already), but also the conditions to upgrade it. A button allows you to access a comparison between the current level and the next one, as well as the upgrade cost.
Indeed, once the conditions are fulfilled, all the upgrades require an investment and a building time. The payment can be done with cash or Tokens. As for the building time, it can be brought back to 0 with Tokens, which remains true even after the building has started. The cost is proportional to the remaining time.
Careful, as there can be only one infrastructure under construction or being upgraded at once.
To get an idea of what are the effect of upgrades, you can see the sections dedicated to each infrastructure.