If you add this code to a wikipedia article [[File:Map of the route of Edward III's chevauchée of 1346.svg|left|thumb|250px|alt=A map of south east England and north east France showing the route of the English army|Map of the route of Edward III's [[chevauchée]] of 1346]]
you will get this

A map of south east England and north east France showing the route of the English army
Map of the route of Edward III's chevauchée of 1346















You can edit the different parts of the code to get different result, e.a. you don't have to have the "alt=x", like this [[File:Calais2015g.jpg|thumb|Badeldin Shogar, a Sudanese migrant, at the Jungle in October 2015]]
which gives this

Badeldin Shogar, a Sudanese migrant, at the Jungle in October 2015










Look at the code in different articles.

If you click on that image or the "Enlarge" symbol down to the right it takes you to an enlarged version of the image. Down to the right you can click on More details which takes you to the description page at commons. If you on the other hand right click on the image and choose "Open link in .." or similar you end up on a description page of that image within wikipedia (the image is not really "at wikipedia", it's a generated copy from commons). A bit down there is a link description page there which takes you to the description page at commons.
Commons and wikipedia has different objectives (wikipedia, commons) but ALL (some exceptions) media is now days at commons, it's supposed to be so. There are some differences between wikipedia and commons regarding what can be uploaded to the two different places, it's mainly about different licences regarding copyright and what they allow you to use an image for.

UPDATE

Look at an image desription page like this, Map of the route of Edward III's chevauchée of 1346 go all the way to the description page at commons. At the top below the file name a bit there is a row with symbols and links. Find the "W" symbol "Use this file "on a wiki"" and click on it. Then you will get two sets of code which is what you need to insert that image.
To insert an image in an article at wikipedia You will never need to download and upload any image (or any type of media), it's all driven by database and code, this is my knowledge as now.