What is the correct order or proceedings in a criminal trial?

Accusation, Arrest, Bond (sometimes), pretrial, trial on guilt/innocence, punishment (should it be necessary).

For the trial itself, presuming it is a jury trial, it begins with jury selection, then the State's opening statement, then the defense's opening statement (or defense can reserve opening statement to prior to their case in chief). Then the State puts on their case in chief. The state rests. The Defense puts on their case in chief, then rests. The state can either rebut, or close. If the State rebuts, the Defense may do the same, or if the state closes, the defense then closes. Closing arguments come next, in which the state has the opportunity to go both first and last, and the defense goes in the middle.

The jury then deliberates and determines whether the defendant is guilty or not guilty. If the verdict is guilty, then punishment phase begins in a similar fashion (with the same jury, or to the judge if the defendant wishes).

These procedures are for Texas, and may vary slightly in other states, but would be similar if not the same.