After installation startup X-Plane.
In X-Plane's startup menu place yourself at a busy airport.
Maybe you want to check coverage at the web site of OpenSky Network first: You will at maximum see the same aircraft as show on their page.
No idea? Try EDDF, LSZH, KLAX, or OMDB: They have a pretty good coverage also of ground traffic. To make things perfect choose a gate or ramp position for your own aircraft rather than a runway...you don't want to be in the way of starting live traffic, do you?
Start your "flight"!
Live Traffic should welcome you with a short message on the screen. Message output is generally in the top right corner.
If you run XSquawkBox, X-IvAp or any other multiplayer client in parallel please read about that now.
Switch to Tower View [Shift-5] and maybe from there even to Free-Camera [c] to roam around and watch.
Messages appear in the top right corner informing you about the fact that live data is being requested and that the buffer (hopefully) starts filling up.
As soon as it says "...displaying 1..." there really is a new aircraft in the air...somewhere.
You can use an index to see aircraft information:
Open an A/C Info Window via the menu
Plugin > LiveTraffic > Aircraft Info...
The cursor blinks in the A/C key field, the only editable field of the window. Just type "1" and hit Enter. This shall display the first aircraft in LiveTraffic's list of visible aircraft. (Guess which aircraft would be shown if you had entered "2"...)
If you still have no idea where to look check the Bearing | Distance information in the A/C Info Window and look there.
Tip: you can activate camera info in X-Planes
Settings > Data Input & Output, that'll also show you your camera hdng.
You can open as many A/C Info Windows as you like.
The A/C key field in the A/C Info Window also allows you to enter any of the following information to find an aircraft, useful if you want to see details for an aircraft you see on screen or on the radar screens of the flight tracking web pages:
Transponder hex code
Registration (tail number)
If you select the AUTO checkbox then the window chooses the closest aircraft roughly in the direction you are looking.
Give LiveTraffic one or two minutes time to collect and buffer data and stabilize derived flight paths, and just enjoy watching traffic for a while.
Open X-Plane's internal map: All of LiveTraffic's planes appear there, too.
You'll notice that the aircraft come with yellow labels. You can configure the content of it in the settings. By default it contains a/c type, a unique identifier (flight number, call sign, registration, or transponder hex code, whatever is available first in this order), altitude, and speed. You can type the unique identifier into an A/C Info Window for getting infos on an aircraft of your interest.
At the bottom of the Aircraft Info Window click on Camera...and you hop onto that plane's tail and follow it's movements (see here for more info).
Toggle the Visible checkbox: The plane will disappear and reappear, which you can use to make yourself a slot in a busy queue waiting for take off (see here for more info).
And when you find or make that gap - take off yourself and chase the others...or just link into the chain of approaching aircraft and be a good chain link. Check your TCAS...it might work!