Correct: When you go to the supermarket, please buy eggs, milk, pears, and carrots.
This sentence begins with a dependent clause. A dependent clause should be separated from the independent clause when it is used as an introductory phrase. Commas are also used to separate items in a list. There is some question as to whether or not the comma before the and is needed, but either option is acceptable.
Correct: I plan to go skiing with my sisters, Charles and Boris.
The names Charles and Boris make an appositive phrase that names who the sisters are. An appositive phrase should be set off with commas.
Not Correct: Mariana hopes to study chemistry geometry, and Italian.
This sentence is not punctuated correctly. There should be commas to separate the items in a list. This means that there is a comma missing after chemistry.