Who should start the sprint?

The new Sprint starts immediately following the last Sprint.  As soon as your Sprint Retrospective ends the last Sprint, Sprint Planning kicks off the new Sprint.  The entire Scrum team should be present in Sprint Planning to start the Sprint.

The Scrum Master makes sure the rules of Scrum are followed.

What does the Scrum Guide have to say about when each Sprint starts?

Thanks for your responses! Of course the sprint starts right after the previous one was concluded.

After posting this question I've realized, that I made a mistake -  what I actually meant to ask was: 

"Who should start the Daily Scrum and who decides on that" - sorry for confusion.

Anybody would disagree, that it is entirely up to Development Team to decide?

Who should start the sprint?

If you mean, "Who should initiate the very first sprint?" or "How should a team come together to start sprinting in the first place?" then this is not addressed in the Scrum Guide, except for the implication that if you are not sprinting, then you are not doing Scrum.

Therefore if this is what you meant by your question, I would ask these questions to help guide toward an answer:

• What development approach, methodology, or framework is the team using now?
• Is the team experienced with Scrum? (And was it Scrum, Scrum-but, Scrum-and ...?)
• What problems is the team facing with the current approach and hoping to solve?
• Who has suggested the team try Scrum? Did it come from within the team or outside of it? By "management"? From an appointed Scrum Master?
• Is there an identified Product Owner (and some product vision, however vague or incipient)?

I imagine many Scrum Masters would suggest beginning the first sprint as soon as the minimal components necessary to use Scrum are in place, even if some (e.g., Product Backlog) are initialized in the first Sprint Planning.

In my team Daily Scrum is started by someone from the team. Not always SM (who is also part of the dev team).

Thanks for the clarification, Szymon.

Since only the Development Team participates in the Daily Scrum, then they should indeed be the only ones deciding how the event is started and run (within the guidance of the Scrum Guide).

The Scrum Master may facilitate as requested or needed. Commonly this may occur early on, with a new team or team members new to Scrum.

The Daily Scrum just starts at the time and place the Development Team agreed upon. ;)