You might be interested in checking out this older answer I wrote about the 1996 election.

I'll also follow that up with a link to the OSCE Report for the election. Their major findings pretty much reflect the general consensus about how it was conducted - the media landscape (which is where most of the campaigning occurred) basically abandoned any pretense of being non-biased. Communist media outlets were uniformly negative about Yeltsin, and non-Communist media outlets uniformly negative about Zyuganov. As the report also noted, a lot of money was spent by the campaigns that skirted campaign financing laws. Yeltsin himself arguably broke Russian elections law by using his office as a means to campaign, and government officials often were open about being pro-Yeltsin.

So there's a serious question whether the election was all that "fair". But then again - the elections were actually held according to schedule, and this was not something that was taken for granted, especially as there were rumors in May that the second round would be cancelled (it seems that this was mostly urged by General Alexander Korzhakov of the Presidential Security Service, although Korzhakov claims it was Yeltsin and Prime Minister Chernomyrdin who were discussing this). 11 out of 17 candidates met the qualifications to run as presidential candidates, none were thrown in jail or had mysterious "accidents", and there is no evidence of widespread vote-rigging or fraud. Many of the issues associated with casting ballots, like "family voting" (where the head of household, usually the man, voted on behalf of all registered voters in the family) were actually holdover practices from Soviet elections. The Americans and/or CIA did not rig the election either, although President Clinton very openly pushed for an IMF loan to Russia that Yeltsin very openly used to pay government salaries, and several American election campaign consultants were hired, although it's unclear just how much good those consultants actually did to anyone.

One last note about Yeltsin's polling. It is absolutely true that Yeltsin was polling around 5% in late January. That looks like that mostly comes from VCIOM polls (that's the Russian Public Opinion Research Center, although I can't find 1996 data directly on their website, but rather on a different, ancient late 90s site. Anyway, yes, this put Yeltsin down towards the bottom compared to other likely candidates, especially the front runner, Zyuganov. However, Zyuganov was "frontunner" with only a few percentage points' more than Yeltsin, depending on the poll. Zyuganov actually had higher negative ratings at the time than Yeltsin did. Respondents expected both Yeltsin and Zyuganov to make it to the runoff round, and the expected votes there were much closer, but with Zyuganov ahead of Yeltsin at that point in the polling. However, a lot of respondents at that point did not want to vote for either or were undecided. So I think it's helpful to mention that because it was less that Yeltsin was a lost cause that could only have won from massive rigging and more that there was a crowded field of candidates with a very disenchanted electorate, and the two likely runoff candidates (Yeltsin and Zyuganov) had very high negative ratings.