how do I know if my MacBook is operating by wifi or my ethernet that I just connected for the first time?

Go into System Preferences > Network. It will show you that both or one are connected. The one highest in the hierarchy that also has the green circle next to it will be the one connected.

If you want to rearrange them, click the gear icon at the bottom the click Set Service Order, and you can rearrange which one is connected first if both are connected.

Hope that helps!

Not sure how your question would involve an AirPort Express, AirPort Extreme or AirPort Time Capsule.....the products that we support in this forum.

Click on System Preferences (gear icon on the dock)

Click on Network

Whatever connection is at the top of the list is the current connection

If you always want the Mac to operate using Ethernet when both Ethernet and wireless are available, then click on the gear icon at the bottom of the list, then click on Set Service Order.

Make sure that Ethernet is at the top of the connection order list. If it's not, drag it there.

Another way to make sure that you are connected using Ethernet, is to turn off the WiFi on the Mac, using the WiFi menu at the top of the Mac's screen.

There is no reason to have WiFi on the Mac "on" if you have a wired connection to the Mac.....and.....having both Ethernet and wireless active at the same time can create conflicts and confusion on the network.

Turn the wifi off, if you are using ethernet the web will continue to be available, if not you were on wifi. Or do it the other way around, unplug the ethernet etc.