Let's for the sake of argument assume that you're an unremarkable American communist. I say this because the easiest way to be guaranteed a good life in the Soviet Union would be spying, and mostly getting away with it: Klaus Fuchs, one of the most important atomic spies, ended up as director of a research institute in East Germany, albeit after 9 years of prison in the UK. More generally, having information of value, or being yourself of propaganda value, would help your chances.

(The rest of this comment is a summary of The Defector Study, Staff Report of the Select Committee on Assassinations, which was produced as part of the Kennedy Assassination investigations - Oswald was a former defector himself)

Out of the 10 (11, two traveled as a group) defectors besides Oswald identified from 58-64, none of them defected from the borders of the United States: 4 of them overstayed tourist visas, 2 were military in Germany and defected initially to the DDR, two came via Austria and Czechoslovakia, one was working on the 59 World's Fair and one was via the PRC and Poland. Generally, once present in the USSR, you would notify local officials that you wanted to defect and draw up a statement requesting political asylum; if you're a communist and labor organizer, you probably can come up with convincing reasons for this.

If this was approved, defectors' lodging was arranged initially by the state, along with small financial assistance - probably about 100 rubles/mo, though this varied (this would be a third of a Soviet student's stipend). Finding employment was also done with state assistance.

However, judging from this sample, your long term odds weren't that great. Out of the 10, 7 returned to the United States eventually, either by getting a normal Soviet exit visa and returning as an American, or being admitted as a Soviet citizen. Two of them are unaccounted for in the report; one may have gotten a work visa in England. The last was hospitalized for drunkenness and died about three years after his defection.

tldr: On average, you would gain entry to the USSR, ask for asylum, and spend some time working before you decided you'd made a mistake.