Trump in general has been supportive of Putin and the Russian government, there are several specific policy reasons that they supported him.

Trump will weaken US commitment to NATO
While Trump in general has been supportive of Putin and the Russian government, there are several specific policy reasons that they supported him.

Trump will weaken US commitment to NATO

For Vladimir Putin, the election of Donald Trump may undermine the NATO military alliance. Trump has said that the U.S. would not automatically defend its treaty allies and that we might withdraw forces from Europe and Asia. This weakening of the U.S. commitment to NATO comes at a time when the military alliance is seeking to deter Russia from threatening to annex the Baltic nations, as it did the Crimea.

http://www.nydailynews.com/opinion/richard-clarke-america-enemies-influencing-election-article-1.2725718

Trump will consider recognizing Crimea as part of Russia
Putin has rational motives for wanting Trump to win: Trump champions many foreign policies that Putin supports. Trump's most shocking, pro-Kremlin proposal is to "look into" recognition of Crimea as a part of Russia. President Barack Obama and nearly every member of Congress — Republican and Democrat — have rejected that idea vigorously. Only Afghanistan, Cuba, Nicaragua, North Korea, Syria and Venezuela have recognized Russia's annexation of Crimea. Naturally, Putin would love to see the United States join that list.

http://www.chicagotribune.com/news/opinion/commentary/ct-putin-wants-donald-trump-win-20160819-story.html

Trump has supported other Russian military actions, such as against Syria
Trump likely doesn’t know it, but his (absurd) idea that ISIS could mount a coup against the U.S. government from within the country is once again a gift to Putin. The Russian leader has been justifying his decision to send Russian forces to Syria on the basis that it protects Russian citizens from future terrorist attacks and the Russian government from destabilization.

http://www.thefiscaltimes.com/2015/10/05/Why-Donald-Trump-Vladimir-Putin-s-Favorite-Presidential-Candidate

Tecnom3:
Trump has supported other Russian military actions, such as against Syria

Russian military actions against Syria as how? Is Russia fighting against the sovereign State of Syria or the liver-eating & head-chopping terrorists propped-up, funded & armed by Amerika to destabilize Syria?

When will the MSM realize that we - most of us - are no longer taken in by their manipulative propaganda & spin of their brain-dead politicians any more?

Their constant barrage of propaganda blaming Russia for everything that the West actually were responsible for is, and will always be - noted & dismissed as cheap lies.

There is more to it than Trump sharing the same ideologies with Putin, remember that USA is a Democratic country

How about Hillary wants to fight Russia?

You are getting the Syria part wrong, it is legal for a country to form alliance just like Nato, GCC, AU etc. so Putin fighting for Assad is not the bone of contention.

The bone of contention is that all cease fire agreements have failed primarily because the US and her allies are pushing for regime change in Syria, a position Russia strongly disagrees with hence further escalation of the conflict.

Russia is hoping that Trump will shift grounds in that regards, while campaigning, Trump recognised, Syrian Army, Russia, Iran and Hezbollah as the only forces fighting daesh while the US and GCC are busy replenishing their ranks.