Select the object, context menu and click Shade smooth, then on edges, you select Mark sharp or Clear sharp as you need.
You can smoothen selected geometry with W > Smooth or scale it along normals with Alt + S to make it located under harder / softer angle. That's adding a "smooth mesh" in Maya, adds twice the geometry per iteration and it's not related.
I don't think there's the same operator in Blender, it is, like most of the Blender equivalent its just named in a different way.
Go into edit mode and hit Shift + B and drag the cursor until you have the desired amount. no, that's beveling, maya ahs athe same concept in Mesh tools, bevel again, adds geometry, totally unrelated.
Go to the modifier tab and click:
Add Modifier > Generate > Bevel again, adds a bevel, which changes geometry and destroy uvs, not related to question.
There is the crease tool, which allows you to sharpen the edges by whatever amount you want, and doesn't add more mesh to do it, like the bevel tool does. Just select the edge(s) and press Shift + E , then pull the string you see attached to the mouse until the edges are as sharp as you want them. They will turn pinkish/purple as the crease gets sharper. You can adjust this at any time by pressing Shift-E again and relaxing the string with the mouse.
Nope, that's the crease tool, Maya has the same tool also named crease, and it's nothing like the guy asked.
What has turned me away from Blender has been the answers everywhere. "Not possible" actually means "I don't know how, so ill just say it doesn't exist".
A friend of mine who said was a Blender expert always told me of things that weren't possible to do in Blender, and it turns out not only they exist, but are easier to do that in other software.