How do I Upgrade ships and other things ?

[Facetious]

Just to offer another explaination.

You need your ship to be at a planet with a shipyard. Then select your ship and click the "Scrap, Analyze, Mothball" icon, (it looks like three arrows in a triangular pattern)

Then select your ship again (only one at a time) and click the "Retrofit" button. You'll then get a screen that shows the possible ship designs that you can convert your ship into.

There is a limit to how much of an upgrade you can do, based on the cost of the ship. If the new design costs way more than the current one it won't let you do the retrofit.