Contraband generally got to inmates through three methods.

A. Diverted from within the prison

Many prisons allowed inmates to work various jobs on the inside. Some would take advantage of their access to tools and goods to steal them and resell them to other inmates.

In his autobiography, Malcolm X describes "nutmeg men" who would purchase stolen containers of nutmeg from the kitchen staff and resell them to other inmates during his 1946-1952 imprisonment.

I first got high in Charlestown on nutmeg. My cellmate was among at least a hundred nutmeg men who, for money or cigarettes, bought from kitchen-worker inmates penny matchboxes full of stolen nutmeg. I grabbed a box as though it were a pound of heavy drugs. Stirred into a glass of cold water, a penny matchbox full of nutmeg had the kick of three or four reefers.

Some inmates would also purchase extra rations from each-other, especially during special events such as Christmas where prisoners would be given access to foods that were not available for the rest of the year.

Writer Donald Lowrie describes a "Red" like figure doing this during his 1900-1911 prison sentence, a few decades prior to the setting of Shawshank Redemption.

Some of the prisoners who do not use tobacco wait at the top of the stairs and bargain for pie and cake. Each prisoner gets half a mince pie, which is worth two rations of tobacco. Cake and pork are each worth one ratio.

At the time I worked in the jute mill "Fatty" was the chief merchant as well as the pawnbroker of the prison. On Christmas and other holidays he used to hire agents, on commission, to wait at the head of the stairs and buy pie and other food. By this procedure he would corner thirty or forty pies. Three or four days after Christmas a half pie was worth four or five sacks of tobacco, and "Fatty" always came out a few hundred rations of "weed" to the good. Moneyed prisoners would buy his supply at the advanced rate, and be glad to get it.

B. Smuggled in by correctional officers.

Prison guards were oftentimes paid very little, and in some cases came from the same communities as many of the inmates. This meant many turned to accepting payment from prisoners in exchange for contraband from the outside.

Malcolm X describes graduating from purchasing nutmeg for a high to buying the more expensive, and harder to obtain pharmaceutical drugs from prison guards.

With some money sent by Ella, I was finally able to buy stuff for better highs from guards in the prison. I got reefers, Nembutal, and Benzedrine. Smuggling to prisoners was the guards' sideline; every prison's inmates know that's how guards make most of their living.

Depending on the year and the prison, prisoners caught participating in any kind of trading with guards could find themselves severely punished. Lowrie writes about an inmate caught making ornaments for this purpose.

In January, 1908, a prisoner named R. was caught making abalone shell ornaments in his cell. The Captain of the Yard inferred that he was engaged in making these ornaments for the guards - that he was trading - and the man was sent to the dungeon and placed in the strait-jacket for the purpose of forcing him to divulge with whom he was "doing business." For several days he was kept in the jacket - six hours in, six hours out."

C. Smuggled in by a civilian on the outside.

This method was likely the one that required the most ingenuity of all the options. Inmates were constantly trying to find loopholes in prison policy, and would take any opportunity to have friends and family on the outside smuggle in goods through visitation or mail.

In some prisons, such as Trenton State Prison in the 1930s (now New Jersey State Prison), the yard was close enough to residential areas that inmates could speak to outsiders and receive goods thrown over the walls.

Meanwhile, Lowrie at San Quentin State Prison describes the rampant smuggling of opium and morphine through Christmas gifts during the early part of his sentence.

Some years ago the prisoners at San Quentin were permitted to have food and presents from relatives and friends at Christmas. But when the fight was waged against "dope" this privilege was stopped. It was found that opium and morphine were introduced into the prison that way. On one occasion a roasted turkey disgorged half a pound of opium "dressing." Confections were utilized for the same purpose. Even towels would be soaked in an opium bath, and on being received by the prisoner would be subjected to a re-soaking. The resultant liquid would be bottled up and imbibed by degrees. Some of the schemes for getting the stuff were really ingenious. So the order was issued that nothing would be permitted in the way of presents at Christmas.

Another common method mentioned by Lowrie that remained common into the 1950s was the use of "papers," which means a letter or any other form of paper sprayed by or dipped into a liquid (such as heroin or morphine) which would then be dried and sent to an inmate, who could then rip up the paper and trade the pieces individually to other inmates.

Conclusion

Ultimately, inmates effectively took advantage of any possible opportunity to obtain comforts from the outside. Policies of individual prisons were and are often fairly changing and inmates would have to adapt their tactics to the current conditions in the prison they happened to be in. In any scenario and time period you will definitely find a figure like "Red" who obtains social cachet in the prison through their ability to find ways to obtain goods and contraband.