You can use the word "and" after a comma. Two case exist which warrant the use of a comma before the word "and":
1. Firstly as a serial comma, where there are three or more items in a list of series. Example: Harry has two combs, four toothbrushes, and seventeen facecloths in his bathroom cupboard.
2. Secondly to separate two independent clauses i.e. a section that contains its own subject and verb and can stand alone as a sentence. Example: I will go to the shops, and I will buy chips and ice-cream. If we delete the subject in the second clause (i.e. "I"), we can then also drop the comma i.e. I will go to the shops and buy chips and ice-cream. The second part of the sentence is now not a stand-alone clause anymore.