It's a strange one, as some of the Normandy research upgrades are essential, while others are superfluous. With how they're presented in-game, we're not surprised that some are confused about what ship upgrades actually do.
The ship upgrades are filed into the research menu under the Ship Enhancements option. As soon as Mordin is on board the ship, a range of characters including Miranda, Jacob, and even Doctor Chakwas will begin suggesting Normandy upgrades to you.
In ME2, the Normandy SR-2 Ship Upgrades can be accessed through the science bay as soon as you've recruited your head of science, Mordin, via the Dossier: The Professor Mission that's granted right at the start of your free-roaming access to space where you can choose your own mission order.
Character growth is a solid staple of role-playing games, and arguably one of the most important characters of Mass Effect 2 is the Normandy SR-2 - and in finest RPG tradition, the Normandy gets a range of ship upgrades that you'll want to consider spending your hard-earned resources on.