My grandparents were both german. I am 23 years old, can I get a german passport

Most probably not.
Usually at least one of your parents must have been German when you were born to be eligible for citizenship.

Not because your grand parents are germans it means you will be automatically german too. If one of your parents are german then you are automatically german citizen too. But if you want to have a german passort there's a long way to go. First of all you hhave to be resident in germany for 8 years ( if you are not married to a german person but if you are married to a german person you need to be in germany for 2 to 3 years) you have pass all the exam B1 and einbuergerungstest. Aside from that, you have to speak german too. For more information. Ask the german authority. Thanks.

I have just got German citizenship and passport for my wife and daughters, so here is the deal:
If your grandparents were Germans, you might be entitled for German citizenship and passport.
You will have to obtain your grandfather's birth certificate, and their marriage certificate from Germany. After that you will need to contact the German embassy, giving them the following documents:
Your grandparents documents I've stated above, your father/mother's birth certificate, and their marriage certificate, and your own birth certificate.
They will review your request and let you know if you are eligible. THERE ARE GOOD CHANCES THAT YOU ARE!
The embassy will guide you on your next step. The whole process might take up to one year.
To obtain the documents from Germany, I used the website www.germany-service.com