The International Federation of Pickleball "owns" the official Pickleball rules, which were adopted and updated from those set by the USA Pickleball Association. You can keep up with those rules on the USAPA site, here: HERE. That page shows the latest revisions to the rules, and provides a direct link to the 50+ page PDF with the full rule-set.
Newer Pickleball players need not digest the full rule set until they have reached a proficiency close to that of tournament-level players. Up to that point, one will do fine to understand a simplified set of rules such as these below. (Credit to the AZPickleballFun.com website for the original version of this - check out that site for more good stuff!)
A Game is finished when one player or team reaches 11 points and is leading by at least two points. If the score is tied at 10-10, then the game continues until one player or team wins by two points. Players usually switch sides after each game.
Serving in Pickleball is similar to Volleyball - a player or team only scores points when serving.
Both feet must remain behind the baseline until after the ball is struck.
Players announce the score prior to serving (call the server's score first)!
The serve must be made with an underhand stroke (moving in an upward arc) so that contact with the ball is made below waist level while the paddle head is below the top of the wrist.
Serves are to the diagonal half of the opposite court (the "service court").
Serves must land beyond the "non-volley zone" near the net (a.k.a. the "kitchen") and inside or on the far baseline.
Each player is allowed only one serving attempt unless it is a "let" serve (which " like tennis " occurs when the serve hits the net and still lands in the correct service court) A Let is played over.
Each player continues serving when he wins a point.
The player on the right serves first and continues to serve while making points.
THE FIRST SERVER of a new game, after failing to make a point, turns the serve over to the OTHER TEAM instead of his partner.
Thereafter, both members of each team will have a service turn before the ball is turned over to the other team.
When a point is scored, the serving team swaps sides on their court before their next serve. (The receiving team DOES NOT.)
TIP for keeping track of the score: In doubles, your team's score is always even if you are serving on the side of the court you started the game on. Otherwise it's odd.
Serve from the right when you have an even number of points, otherwise serve from the left. (Receiver positions to match.)
Non-Volley Zone (a.k.a. the "Kitchen"): To volley a ball means to hit it in the air without letting it bounce. All volleying must be done with the player's feet behind the non-volley zone that's within 7 feet of the net.
The zone marking line is part of the Kitchen.
Making contact with the Kitchen during/the act of hitting a volley (including momentun after a volley) is a fault, and point or serve is lost.
Contact includes feet, hands or other part of the body or paddle or clothing.
If you are inside the Kitchen, you are not outside until BOTH feet touch outside the kitchen. Example: you step into the kitchen just before a ball is hit your way so you jump out - both feet must touch before you can volley back.
Double Bounce Rule: On the serve, the receiving team must play the ball off a bounce, AND THEN the other (serving) team must ALSO play that ball off a bounce. Volleys are then allowed after the two bounces have occurred.
Playing the ball: The ball may only bounce once per side. After the ball is hit by a player, it must travel to the other side of the net. The sideline and baseline is part of the playable court.
Faults: Failure to return a playable ball is a fault. Some other faults:
Serving the ball into the net, an incorrect area or out of bounds.
Server swings paddle with the intent of serving but misses the ball.
Volleying the ball before it has bounced once on each side.
Hitting the net with your paddle or body.
Violating the Kitchen on a volley (see above)