Overview

Applications for a trial adjournment may be made by the Crown or the defence.  It is undisputed that whether an adjournment or a postponement should be granted or not is a discretionary matter for the trial judge:
 Manhas v. The Queen, 1980 CanLII 172 (SCC, [1980] 1 S.C.R. 591; R. v. Barrette, 1976 CanLII 180 (SCC), , [1977] 2 S.C.R. 121, 29 C.C.C. (2d) 189; R. v. Darville, (1956), 116 C.C.C. 113 (S.C.C.); R. v. MacDonald, 1998 CanLII 18016 (NL CA), [1998] N.J. No. 340 (QL) (C.A.) [reported 132 C.C.C. (3d) 205].
The leading case governing trial adjournment applications is that of Darvillev. the Queen, (1956) 116 C.C.C. 113 (S.C.C.) which sets out a straightforward three-part test. 
Though Darville remains foundational, the test has been elaborated and expanded upon and may, it appears, include such additional factors as the consideration of the public interest in having a trial on the merits (including the related consideration of the seriousness of the offences charged), and whether there would be a lack of significant prejudice to the accused.
Further—in my opinion—where the defence seeks the request, the accused’s right to full answer and defence and even the right to a fair trial, section 11(d) of the Canadian Charter of Rights and Freedoms,may be engaged. 
For an overview of the right to full answer and defence see R. v. Mills, [1999] 3 S.C.R. 668
Trial Adjournment – The Darville Test
On the elements to be considered by a judge when asked to grant an adjournment of a criminal trial due to the absence of a witness, the Supreme Court of Canada provided some guidelines in 1956 in R. v. Darville:
( 1)   that the absent witnesses are material witnesses in the case;
(2)   that the party applying has been guilty of no laches or neglect in omitting to endeavour to procure the attendance of these witnesses;
(3)   that there is a reasonable expectation that the witnesses can be procured at the future time to which it is sought to put off the trial.
R. v. Darville (1956), 116 C.C.C. 113.
Second Branch of Darville:  Neglect in securing the attendance of the witness

After properly serving a subpoena on a witness, there is no additional onus on the Crown to follow up to assure a witness’ attendance at trial.
R. v. M.W.W., 2015 ABPC 271 (CanLII).
But—
Delaying the service of subpoenas for witnesses until just shortly prior to the trial date is a highly prejudicial factor on the issue of laches to a party seeking an adjournment of trial based upon the unavailability or non-attendance of a material witness.
The fact that a subpoena has been served does not, in and of itself, mean that a party is not guilty of laches and therefore presumptively entitled to an adjournment and the issuance of a material witness warrant when the witness is not present for the trial.
R. v. E.O., 2016 YKTC 52.
Third Branch of Darville:  Was there a reasonable expectation that the witness would be present at a future date?

Often trial adjournment requests happen on the day of trial and the applicant has little or no facts as to why a witness has failed to attend. Often it will not be possible at the time of the application for the applicant to provide evidence as to a reasonable expectation of future attendance of the witness, or the reason for non-attendance so trial courts have been instructed to permit the party applying for the adjournment time to make reasonable inquiries in that regard.
In R. v. A.T. [1991] AJ No.1131 (QB), McDonald J commented:
As for [the third branch of Darville], it will commonly be impossible to offer any evidence that if an adjournment is granted there is a reasonable expectation that the attendance of the witness on a future trial date can be procured. Whether there is such a reasonable expectation may depend on a variety of factors which cannot be identified at the time the witness has failed to appear. Is his failure to appear due to his having met with an accident or illness? If that is known, obviously, an adjournment will be granted; ordinarily it will not be known and cannot be discovered until inquiries are made. Is his failure to appear due to forgetfulness on his part? That cannot be known and it will not be known until inquiries are made. Is his failure to appear due to his having been intimidated by the complainant or by someone on the complainant’s behalf, or because the witness has decided without being intimidated that he does not wish to testify against the accused? That cannot be known and it will not be known until inquiries have been made. In all these instances refusal to grant the adjournment may be inconsistent with the interests of justice, and may be the result of an undue readiness to assume that the failure of the witness to appear has been due to circumstances which will not be overcome if the party seeking the attendance of the witness is granted the adjournment.
In cases involving serious personal injury where the complainant does not attend, courts must permit the Crown to take reasonable steps to ensure that the absence of the complainant was not due to intimidation or fear.
 R. v. Henry [1987] OJ No.947 (CA), R. v. M.V. [2004] Q.J No.9875 (CA);
See also R. v. Baez, 2014 ONCJ 484 (CanLII).
Additional Factors for Consideration

The list of factors set out in Darville is not exhaustive.
The Court may also consider other relevant circumstances such as the gravity of the charges, the number of previous postponements and the consequences of a postponement for the accused. Ultimately, the decision whether to grant the adjournment must be made in the light of the realities of each case and shall be consistent with the interests of justice.
R. v. G. (J.C.),2004 CanLII 66281 (QC CA) at para 12,13.
Seriousness of the offence
In R. v. R.J.J., 2003 ABQB 851 (CanLII) the seriousness of the charges was a factor considered by the court in granting the adjournment.
The more serious an allegation is, the more compelling the public interest in assuring that it is heard on its merits.  By the same token, the more serious an allegation, the higher the expectation the court has in expecting that all branches of the Crown will ensure that the case can be heard on its merits a very serious offence.  As such it is important that it be litigated; conversely, the Crown must exercise more diligence in order to ensure that the witnesses are prepared to attend at trial.
Non-attendance of the central complainant often occurs in domestic cases. Given the public interest in cases of alleged domestic abuse, the Crown must be permitted to take reasonable steps to determine the cause of the non-attendance whether or not there’s been serious injury.
R. v. Khasria[2013] OJ No.5040 (SCJ); R. v. Henry.
Even evidence of a voluntary absence does not end the matter in the domestic context. “… to suggest that a voluntary absence can defeat the public interest in a trial on the merits in a domestic abuse case, is to send the wrong message about domestic abuse – a message that domestic assaults that are not as serious as others…”
R. v. Khasriaat para 64; see also R. v. Baez, 2014 ONCJ 484 (CanLII).
Prejudice
In R. v. R.J.J., 2003 ABQB 851 (CanLII) the prospect of a short further delay was not considered to be overly prejudicial to the accused and was a factor considered by the court in granting the adjournment.
No party, be it the Crown or the accused, is entitled to a postponement simply because one has not been previously requested, as if somehow such a request was analogous to the peremptory challenge of a juror which must be granted as a matter of course. Any application for a postponement must stand or fall on its merits, and for no other reason.
R. v. G. (J.C.),2004 CanLII 66281 (QC CA) per Hilton J.A.(dissenting)
What If the Crown attempts to stay the proceedings in order to avoid the trial adjournment?
Where the Crown is unsuccessful in its application for a trial adjournment due to the non-attendance of a material witness, the effect of the Crown staying the proceedings instead of having the accused arraigned would be to circumvent an inevitable acquittal.  Having failed to obtain an adjournment, the stay would effectively achieve what had just been refused.   Such conduct could potentially support an abuse of process application.
Procedure on the Application

An adjournment application is not a trial and the strict rules of evidence do not apply. The court may receive credible and reliable evidence from a witness including reference to information provided by others. That evidence may be challenged in cross-examination.
Where an adjournment application is contested, it’s preferable that the Crown call the officer-in-charge of the case or other witness who can provide evidence relating to the Darville criteria. This provides a proper evidentiary foundation for the application and preserves the right of the defence to cross-examine on those issues.
See R. v. Baez, 2014 ONCJ 484 (CanLII), per  Kenkel J.
In R. v. Baez, the Crown called an officer assisting with the case who provided an overview of his own efforts and the efforts of other officers to locate and serve the witness. The defence objection to the hearsay nature of the evidence was overruled.