The same way you would support a president you did vote for: with caution, questioning, acceptance, and respect. Whether you voted for someone or not, you aught to view their decisions with certain amount of healthy questioning. I’ve included a few quotes below to further explain what I mean.
“Patriotism means to stand by the country. It does not mean to stand by the President or any other public official save exactly to the degree in which he himself stands by the country…
“Every man who parrots the cry of ’stand by the President’ without adding the proviso ’so far as he serves the Republic’ takes an attitude as essentially unmanly as that of any Stuart royalist who championed the doctrine that the King could do no wrong. No self-respecting and intelligent free man could take such an attitude.”
Author: Theodore Roosevelt. Works, vol. 21, pp.316, 321.
God provided that in this land of liberty, our political allegiance shall run not to individuals, that is, to government officials, no matter how great or how small they may be. Under His plan our allegiance and the only allegiance we owe as citizens or denizens of the United States, runs to our inspired Constitution which God himself set up. So runs the oath of office of those who participate in government. A certain loyalty we do owe to the office which a man holds, but even here we owe just by reason of our citizenship, no loyalty to the man himself. In other countries it is to the individual that allegiance runs. This principle of allegiance to the Constitution is basic to our freedom. It is one of the great principles that distinguishes this `land of liberty’ from other countries.
Author: J. Reuben Clark, Source: Improvement Era, July 1940, p. 444
No matter the decision, political party or other persuasion of the president, our allegiance must lie with the Constitution on every issue.