How do I follow a tail number?
Open search and type the registration — an N-number such as N7811T — or the callsign the aircraft is flying under, then follow it. The aircraft pins to your strip board and holds a strip there whether or not it is airborne, so the board is a list of aircraft you care about rather than a list of flights happening right now.
TallyAir pushes a notification when it next goes airborne, so you know to look up before it is overhead rather than after. Open the push and it opens that strip: altitude, ground speed, squawk, and the track flown so far.
Following is also what builds your log: every flight that aircraft makes turns up there, worked out from what you follow rather than from anything you file yourself.