I answered a similar question a little ways back. To pull out the relevant bits here:

Was there US interference? Depends what one means by "interference". Yeltsin negotiated a favorable loan from the IMF at the beginning of 1996, and used it for such things as paying government backwages. Bill Clinton was publicly very supportive in making sure that the loan was made available to Yeltsin. This sounds like nefarious meddling in retrospect, but it was a public campaigning point on Yeltsin's part - he was the one who could negotiate the good deals with the West to get people's wages paid.

American campaign advisers were also hired by Yeltsin, but this in contrast to the IMF loan was kept relatively quiet. The advisers were George Gorton, Joseph Shumate and Richard Dresner, who had all worked in various capacities for the then governor of California, Republican Pete Wilson. The role these consultants had is debatable - they claimed they taught the Yeltsin campaign how to run a modern campaign, and the Yeltsin campaign noted that they spoke no Russian, took six-figure payments, and didn't offer any strategies beyond what the campaign had already decided. It's also worth noting that US political consultants have assisted any candidates in the former Eastern Bloc (and beyond) who are willing to pay.

(Plus...) the elections in 1996 were relatively free and fair in that the votes were not fraudulent, although Yeltsin won the second round largely by coming to understandings with major Russian military figures and oligarchs, who then publicly supported his re-election. Although large chunks of the Russian population and elite were unhappy with Yeltsin, they were less than enthusiastic about a Communist victory, and eventually gave Yeltsin enough support to win 15 percentage points and more than 10 million votes more than Zyuganov.