At the start of the game, just move the Queen off the back rank to connect the Rooks.

Only throw the Queen into an attack if the enemy pieces can't bother it.

[Event "Goteborg SSK 40th Anniversary Group A"]
[Site "Gothenburg"]
[Date "1920.08.18"]
[Round "12"]
[White "Rubinstein, Akiba"]
[Black "Maroczy, Geza"]
[Result "1-0"]
[ECO "D63"]
[Annotator "Regis,Dave"]
[PlyCount "75"]
[EventDate "1920.08.02"]
[EventType "tourn"]
[EventRounds "13"]
[EventCountry "SWE"]
[SourceTitle "HCL"]
[Source "ChessBase"]
[SourceDate "1999.07.01"]
[SourceVersion "2"]
[SourceVersionDate "1999.07.01"]
[SourceQuality "1"]

1. d4 Nf6 2. Nf3 d5 3. c4 e6 4. Bg5 Be7 5. e3 Nbd7 6. Nc3 O-O 7. Rc1 Re8 8. Qc2
{The Queen makes a modest first move.} dxc4 9. Bxc4 c5 10. O-O cxd4 11. Nxd4 a6
12. Rfd1 Qa5 13. Bh4 Ne5 14. Be2 Ng6 15. Bg3 e5 16. Nb3 Qc7 17. Qb1 {A retreat
to threaten the Black Queen, which retreats.} Qb8 18. Bf3 Qa7 19. Na5 {!} Bb4
20. Nc4 Bd7 21. Nd5 Nxd5 22. Bxd5 Be6 23. Qe4 {[#] ! The Queen enters the fray,
reinforcing several points of attack at once. The Black pieces are not easily
able to harass her.} Bxd5 24. Rxd5 Rac8 25. Rcd1 Bf8 26. b3 b5 27. Nd6 Bxd6 28.
Rxd6 Rc7 29. h4 {!} f6 30. Qd5+ Kh8 31. h5 Nf8 32. h6 Ng6 {[#] The Queen now
makes the decisive invasion.} (32... gxh6 33. Rxf6) 33. Qe6 Rf8 34. Rd7 gxh6
35. Bh4 Nxh4 36. Qe7 Rxd7 37. Rxd7 Qxd7 38. Qxf8# 1-0

Here are some amazing Queen moves from a top computer game:

[Event "AlphaZero - Stockfish"]
[Site "London ENG"]
[Date "2017.12.04"]
[Round "?"]
[White "AlphaZero (Computer)"]
[Black "Stockfish (Computer)"]
[Result "1-0"]
[ECO "E17"]
[Annotator "Regis,Dave"]
[PlyCount "111"]
[EventDate "2017.??.??"]

1. Nf3 Nf6 2. d4 e6 3. c4 b6 4. g3 Bb7 5. Bg2 Be7 6. O-O O-O 7. d5 exd5 8. Nh4
c6 9. cxd5 Nxd5 10. Nf5 {A well-known gambit line of the Queen's Indian Defence
} Nc7 11. e4 d5 12. exd5 Nxd5 13. Nc3 Nxc3 14. Qg4 {White plays an in-between
move threatening mate: The Queen enters the fight!} g6 15. Nh6+ Kg7 16. bxc3
Bc8 17. Qf4 {The Queen dodges the Bishop's attack} Qd6 18. Qa4 {A remarkable
move: the Queen attacks what looks like an unimportant pawn on c6. Black
chooses to keep the pawn by not developing the Knight.} g5 {White's next move
is really striking: allowing the King to take the Knight when White has only
one (undeveloped) piece aiming at the King's-side!} 19. Re1 Kxh6 20. h4 f6 21.
Be3 Bf5 22. Rad1 Qa3 23. Qc4 {White avoids the exchange of Queens, of course.}
b5 24. hxg5+ fxg5 25. Qh4+ {The Queen takes advantage of a pin to re-enter the
King's-side.} Kg6 26. Qh1 {Another counter-intuitive move, back on the c6 pawn.
} Kg7 27. Be4 Bg6 28. Bxg6 hxg6 29. Qh3 {Eyeing the weak light squares.} Bf6
30. Kg2 Qxa2 31. Rh1 Qg8 32. c4 Re8 33. Bd4 Bxd4 34. Rxd4 Rd8 35. Rxd8 Qxd8 36.
Qe6 {With only two pieces left, White invades, but of course Black is
defending with only one! So Black finally develops the Queen's Knight.} Nd7 37.
Rd1 Nc5 38. Rxd8 Nxe6 39. Rxa8 {The result of the attack is an ending with an
exchange for pawns.} Kf6 40. cxb5 cxb5 41. Kf3 Nd4+ 42. Ke4 Nc6 43. Rc8 Ne7 44.
Rb8 Nf5 45. g4 Nh6 46. f3 Nf7 47. Ra8 Nd6+ 48. Kd5 Nc4 49. Rxa7 Ne3+ 50. Ke4
Nc4 51. Ra6+ Kg7 52. Rc6 Kf7 53. Rc5 Ke6 54. Rxg5 Kf6 55. Rc5 g5 56. Kd4 1-0