For the "new" Dragon Balls on Earth
 After Kami-sama re-merged with Piccolo, Shenlong became no more and the Dragon Balls turned into stone. To revive the Dragon Balls, Goku invited Dende from Namek to be the new Kami-sama. Dende was able to revise the rules and restrictions of Shenlong's power in the revival process.

 1.  Must gather all seven Dragon Balls.
 2.  Chant required (Come out, Shenlong, and grant my wish!).
 3.  Only two wishes per summoning of Shenlong.
 4a.  After the wishes are made, Shenlong will disappear, the Dragon Balls will turn to stone and scatter themselves; they will remain stone for one year.
 4b.  If only one wish is made during the summon and the Dragon Balls turn to stone, they will remain stone for four months, and then Shenlong may be summoned again.
 5.  The Shenlong cannot grant any wishes that are beyond the powers of the creator of the Dragon Balls.
 6.  You can revive anyone or any group of people who fit a certain criteria, if they did not die of natural causes.
 7.  If a person has been revived by Shenlong before, the person cannot be revived again.

For Dragon Balls on Namek
 1.  Must gather all seven Dragon Balls.
 2.  Chant required in the Namek language.
 3.  Wishes must be said in the Namek language.
 4.  Only three wishes per summoning of Puronga (Eternal Dragon of Namek).
 5.  After the wishes are made, Puronga will disappear, the Dragon Balls will turn to stone and scatter themselves; they will remain stone for 130 days.
 6.  Puronga cannot grant any wishes that are beyond the powers of the creator of the Dragon Balls.
 7.  You can revive anyone multiple times, as long as he/she did not die of natural causes.
 8.  You can only revive one person per wish. Dragon Balls of Namek are more powerful and much bigger than the ones on Earth

Please Note: I'm not going to tell info about the Black Star Balls because I don't know much about them, and there isn't a lot of information on them. Sorry.