This isn't worthy of a top-level comment, so I'll end with a clarifying question: With the Soviet Union being a one-party system, there really were no free elections to rig. Are you asking how the communist party chose who was nominated for what?

A few points:

• The general public only got to vote delegates into the Supreme Soviet - this was nominally the equivelent of a parliament, but in practice this organ of government didn't really have any power. The Soviet was basically there to rubber stamp things, especially in the Stalin era. At times it was an avenue for opinions to be aired, but it didn't really have decision making power.

• Now in terms of 'voting for Stalin', only Communist party members had any say in that, and even then for the rank and file it was an indirect thing. Your rank and file voting people into relatively low level committees, which in turn can send people into higher committees and so on till you get to a all-union level party plenum.

• Party membership wasn't necessarily an easy thing to get, especially going into the 1930s and the crackdown on memberships. So the general population could all just join the party so they could have a say. In principle you had to be nominated by an existing member, and you had to have demonstrated certain qualities. In practice this wasn't always the case but we'll get to that.

• Many key positions of authority were subject to confirmation by higher committees. This was often used as a way of showing someone how important you were (ie. my job is so important it had to be confirmed by the regional apparatus, implying you had friends there and that your job must be a big deal. So this could be a filter on who can go up the chain right there, and those positions of authority also tend to be a position to wrangle the votes.

• Another filter was until about 1936 from memory, party committees didn't have secret ballots - you voted for the chairman etc. openly. This was kind of a problem because a local party boss (and his cronies) could be quite powerful. If you vote against them they'll see it and they can retaliate (for example by getting you shifted to a crappier job). Criticism/issues could also be raised with candidates, but again this wasn't really encouraged.

• As to why people further up the chain at the all-union level 'voted' for Stalin... well, keep in mind he wasn't an unpopular guy. Stalin was seen by many as a good worker, a person of substance on ideological issues etc. A lot of people in the party did well under Stalin which naturally generated a bit of loyalty.

J. Arch Getty talks a fair bit about internal party politics and the pressures this could generate in 'The Road to Terror' and 'Orgins of the Great Purges'. The former is a better book in terms of hammering out Getty's main premise, but the latter gets into more nitty gritty detail of what was happening at local levels. More recent biographies of Stalin (like Robert Service's) and Sheila Fitzpatrick's 'Everyday Stalinism' cover the point of his being reasonably 'popular' in his own way, how some people did well out of the Stalin era etc.

Sorry I am a bit late to this one (moving really sucks when you have a compulsive book buying habit!), but to add to the fine answers by /u/Smilin_Dave and /u/International_KB here, there is an important dimension to Soviet elections that needs emphasis. While it is true that Soviet elections were "elections without choice," the Soviet regime lavished an inordinate degree of attention on Soviet elections. The Stalin Constitution of 1937 nominally provided for a secret ballot and a degree of candidates and the state used high electoral turnout to legitimize the grand Soviet experiment. High turnout was also a means of social control by the state as elections verified that the voter was a legal resident of a particular area. Therefore, local officials were often under intense pressure to guarantee a high political turnout. This was one of the reasons why voter turnout typically averaged in the eightieth percentile from 1937 onwards.

While many local CP officials fudged the numbers of turnout, this was a dangerous stratagem if caught. Like political bosses in the West, these local officials would employ various inducements to get voters to the polls. From the Second World War onwards, Soviet elections increasingly assumed a holiday-like atmosphere to attract voters. Similarly, mobile voting booths were often used to make sure that infirm voters could cast their ballots. The intense pressure from the center on these local officials to deliver the numbers gave the Soviet voter leverage in which abstaining from voting gave the voter a degree of power. The various meetings in the run-up for Soviet elections were often a time when the public could petition the officials for local improvements, repair of infrastructure, and airing other grievances. There was also a pronounced uptick in petitions and other requests to the electoral officials and newspapers during election season and some of these entreaties included the threat that if they were not met by election day, these individuals would boycott the election. By the same token, some Soviet voters would sometimes write petitions on the ballots to the authorities. Some of these preserved ballots have patriotic slogans, but others contained personal requests or denunciations of local officials.

Although Soviet elections were not democratic in any formal meaning of the word, they were a channel for political communication between the state and its citizens. Even without any real electoral choice, many Soviet citizens recognized that there was some degree of power in the act of voting and bargained with local officials accordingly.

Source

Jessen, Ralph, and Hedwig Richter. Voting for Hitler and Stalin: Elections Under 20th Century Dictatorships. Frankfurt: Campus Verlag, 2011.