In the inventory screen, if you swap an equipped part for one that isn't, it'll automatically be swapped on your ship assuming that they are both the same type and size.

Step 1: Open the your inventory menu. It's that grey box I made into the icon of this guide.
Step 2: Click on the new part you want on the ship and hit Transfer.
Step 3: Click on the new part and the part you want to swap with it. Then hit Transfer.



See? Simple right?

This will also apply to trading as well. If you buy a new part, and sell an equipped one, they'll swap just as they did here.

Another things that's helpful is if you right click on a part, the game will compare it's stats with any item you hover your mouse over. So you can find the right part to swap much more easily.