The serve and return of serve are the two most important skills. The server starts off in control and it is their first chance to win or lose the point. The return is also the returners first chance to lose or possibly win the point.
Lets cover the serve first.
According to the rules of table tennis:
2.6 THE SERVICE
2.6.1 Service shall start with the ball resting freely on the open palm
of the server’s stationary free hand.
2.6.2 The server shall then project the ball near vertically upwards,
without imparting spin, so that it rises at least 16cm after leaving the
palm of the free hand and then falls without touching anything before
being struck.
2.6.3 As the ball is falling the server shall strike it so that it
touches first his or her court and then touches directly the receiver’s
court; in doubles, the ball shall touch successively the right half court
of server and receiver.
2.6.4 From the start of service until it is struck, the ball shall be
above the level of the playing surface and behind the server’s end line,
and it shall not be hidden from the receiver by the server or his or her
doubles partner or by anything they wear or carry.
2.6.5 As soon as the ball has been projected, the server’s free arm and
hand shall be removed from the space between the ball and the net. The
space between the ball and the net is defined by the ball, the net and
its indefinite upward extension.
2.6.6 It is the responsibility of the player to serve so that the umpire
or the assistant umpire can be satisfied that he or she complies with the
requirements of the Laws, and either may decide that a service is
incorrect.
2.6.6.1 If either the umpire or the assistant umpire is not sure about
the legality of a service he or she may, on the first occasion in a
match, interrupt play and warn the server; but any subsequent service by
that player or his or her doubles partner which is not clearly legal
shall be considered incorrect.
2.6.7 Exceptionally, the umpire may relax the requirements for a correct
service where he or she is satisfied that compliance is prevented by
physical disability.
Note: If the ball strikes the net and continues on to strike your opponents side it is called a “let” and you are allowed to take your serve over with no penalty. There are no limits to how many lets you can have in a row. There also are no penalties (as in Tennis) for lets.
Basic Service in Table Tennis This is a very basic way to start if you have never played before. For many the first couple of levels can be skipped. RT 3:57 https://www.youtube.com/watch?v=NfmPcpi4sfc&t=51s
4 Simple serves for beginners
https://www.youtube.com/watch?v=oL5BQuBuMHY&t=24s&pp=ygUdNCBzaW1wbGUgc2VydmVzIGZvciBiZWdpbm5lcnM%3D
Very good demonstration
Run time is 9.39 minutes Tom Lodziak
This video explains the four basic serves for beginners. There are other videos on each of these serves in other coming blogs or ones that have already been posted on this site.
While the video explains the basic serves you will eventually want to see others on each of the serves separately, and their variations.
They will also explain how to use your body weight, feet, hips etc. to generate more spin.
As you watch videos on youtube or any other site you should watch many on the same topic as they will often explain things differently. If you find one instructor you like you can subscribe to their channel to see more from them on many table tennis skills, exercises, drills etc.
Watch them often as there will be some nuances you will miss the first time through.
This is especially true if you are left handed and find a left handed instructor.
Check back occasionally as more will be added as it becomes available