Xenon ships show as red dots with red tracks on the radar. It's hard to kill a Xenon with lasers alone (presumably their shields regenerate the same way yours do), but missiles cost money.
When you lock on to a Xenon, the 'I'nfo display will tell you his shield and laser values.  If he has 25 Mw shields and 10 Mw lasers you may want to run instead.
Early in the game, you can't outrun the Xenon and you can't catch them if they run away.  After you get your engine "tuned" that will change.
As soon as you enter a new sector, check the Nav Screen for Xenons. If there are too many, turn around and go right back thru the gate.
(Tip)  The MARS, referred to in the manual as ZIPER) is invaluable when you really get to fighting Xenons. It also works for rendezvous-ing with other ships.