To answer your question, we'll have to look at the law, which was voted on by the Council of People of the USSR and Central Excecutive Committee of the USSR in May 7th 1936. That law stated that those who won medals and orders would have to have a monthly bonus added to their salary, discount when paying the rent (anywhere between 10 to 50%), bonus when retiring, in some cases no longer having to pay income taxes, free trip once a year either on train or by ship both ways, completely free public transport (tramways, buses, etc.)

The extra money were paid for those who won and we are going from the most money to the least money. Hero of the Soviet Union = 50 rubles Order of Lenin = 25 rubles Order of the Great Patriotic War = about 20 rubles Order of the Red Banner = 20 rubles All other orders and medals would have received anywhere between 10 to 15 rubles. In cases when somebody was awarded the same award they would have been paid per each award given.

Sadly, this came to a close when in 1948 payments, free transportation were cancelled. Zhukov himself tried reinstating those in 1955. You may ask why did that happen? Some may speculate, that government simply was trying to save some money and to help boost start the economy. In 1956 another vote was put through, where a certain some of money would be paid once a year to each veteran per order/medal, it did not go through. Later "tickets" were given to veterans who participated in WW2, which enabled them to get free items or items with discounted prices. The bonuses were reinstated sometime in 2000 or so, where veterans once again were able to get extra money for their medals. Not all though, some of the awards included in that law are: order of Lenin, order of the Great Patriotic War (I, II, III, and IV), order of Glory.

A bit of a visual for this answer. Orders and medals were given with so "award booklet" which had coupons. Those booklets had name of a person, when said award was issued, ID number, date when the money can be handed out, as well as the sum of money. Here are a few photos of how it looked like.

Those who received the top level awards were in many cases after the war given (if they didn't have it already) preferential access to join the Party. This gave at least somewhat greater access to the ability to buy restricted consumer goods and foodstuffs. The higher up in the hierarchy and nomenklatura system that they could exploit their wartime record to gain, the greater their access to these goods, and the cheaper they would be to purchase.

This was how it was on an informal level for those who had distinguished war records, though some were given much greater privileges as they became 'celebrities' and important figures (think the treatment of Sniper Vasili Zaitsev in Enemy at the Gates).

Alfred Evans thought that the preferential treatment shown to this 'Veteran's generation', who made up a very large number of the low and middle ranks of the party structure, was a significant factor in the disillusionment of the subsequent socialist generations, as the 'glut' of the wartime generation acted to limit the young's access to party status and promotions within the party, as well as the preferential access to goods this provided. At the highest level this can be seen by the pre-Gorbachev leadership (Brezhnev, Andropov and Chernenko), increasingly old men of the wartime generation, dying off with increasing rapidity and becoming increasingly out of touch with the problems of the Soviet Union.