umsteigen
This can mean to change a train or bus.
Ich fahre mit dem Zug von Wien nach München und muss in Salzburg umsteigen.
I am taking the train from Vienna to Munich and have to change trains in Salzburg.
But figuratively it can mean any major change:
Ich habe lange Chemie studiert, bin dann aber auf Physik umgestiegen.
I studied chemistry for a long time, but then switched to physics.
Ich habe jahrelang den Browser von Microsoft verwendet, bin dann aber auf Firefox umgestiegen.
I used Microsoft's browser for years, but then switched to Firefox.
verändern, ändern
Both verbs mean the same: to change something, to turn something into something else.
Ich möchte meine Ernährungsgewohnheiten ändern.
I want to change my eating habits.
Walter ändert seinen Plan.
Walter changes his plan.
Irene verändert die Einstellungen am Gerät.
Irene changes the settings on the device.
Die Krise verändert den Autohandel.
The crisis is changing the auto trade.
umtauschen
This has two meanings:
You have received something and you don't like it. So you go back to where you've got it from and exchange it.
Ich möchte diesen Hut umtauschen, den ich vorgestern bei Ihnen gekauft habe. I nehme stattdessen eine Kappe.
I want to exchange this hat that I bought from you the day before yesterday. I'll take a cap instead.
to exchange money
Mir sind vom Urlaub 300 Pfund übrig geblieben, die möchte ich in Euro umtauschen.
I have 300 pounds left over from my vacation, which I would like to exchange for euros.
wechseln
This also can mean to exchange money:
Mir sind vom Urlaub 300 Pfund übrig geblieben, die möchte ich in Euro wechseln.
I have 300 pounds left over from my vacation, which I would like to exchange for euros.
But it can't be used to exchange something you bought before and dislike now. But instead it can be used if someone or something changes a property or something that belongs to it:
Das Chameleon wechselt seine Farbe.
The chameleon changes its color.
Julia wechselt ihre Handtasche.
Julia changes her handbag.
Additional information
Julia wechselt ihre Handtasche.
Julia changes her handbag.
This means, that Julia did use one handbag before and a different one after she changed them. But all the time she is owner of both of them. Ownership didn't change, just usage.
Julia tauscht ihre Handtasche um.
Julia exchanges her handbag.
This means that she is the owner of a handbag, and she brought it back to the shop. There she gave it back to the salesperson and received a new one. So here the ownership changed.
Julia (ver)ändert ihre Handtasche.
Julia changes her handbag.
Julia keeps the same hangbag as before, but she changed the look of it. Maybe she added a sticker, or she cut off a tassel.
You can not use umsteigen here, because umsteigen is nothing that you can do with something else. It always describes something that happens to the subject itself.