Across the United States, volunteers have been offering their helping hands: * During the last seven years Dr. Joseph Hieu, a Chicago high school teacher and Board of Education member, has helped 1,000 Indochinese refugees assimilate into US culture. He has founded five housing projects for refugees - one of which is now his home.
* While many retirees are out on the golf course or relaxing in the backyard, Thomas Dibblee is mapping the rugged back country of southern California, at his own expense, for the US government. Among other things, he has produced detailed geological maps of the Los Padres National Forest and a report on the Santa Ynez watershed.
* In Harlingen - a south Texas town near Mexico - Frank Ferree was known as the Border Angel. During World War I, Mr. Ferree had vowed to spend his life helping those less fortunate than he was, and he spent the rest of his 94 years scrounging food and clothing for the poverty-stricken communities around his Harlingen home.
These volunteer efforts, along with 17 others, have been tapped for the 1983 President's Volunteer Action Awards, presented Wednesday at a White House luncheon.
The Reagan administration has drawn continuous criticism from Democrats for the effects of its policies on America's less-privileged members. The President's advisers concede that the ''fairness'' issue is a politically troublesome one.
But Reagan has consistently said he believes private groups should shoulder more of the responsibility for citizens who need help.
''It is important that the private sector assume a more active role in solving community problems. In this way the proper balance between public and private responsibilities can be restored,'' said the President in a statement that coincided with his bestowing of the Volunteer Action Awards.
The awards were cosponsored by ACTION, the White House liaison with volunteer efforts; and Volunteer: The National Center for Citizen Involvement, a private group with some politically well-connected Republicans on its board.
And it was Volunteer, not the White House, that did much of the work leading up to Wednesday's awards. The group's contacts across the country produced a list of 2,000 nominees; the most deserving of these were then screened by Volunteer's staff.
ACTION and Volunteer board members jointly picked the 20 winners from 80 finalists.
Many of the winners, such as Ferree (who passed away March 11), provide traditional forms of aid to those who have fallen between the cracks of society: the poor, the handicapped, the low-income elderly.
Others, such as Dr. Hieu, have responded to the problems of immigrant groups whose culture is vastly different from that of their adopted country. Dr. Hieu was himself a refugee in Vietnam when he was only seven years old - and he says he donates his efforts now because he doesn't ''want to see any other child go through the same experience.''
Still others, such as Thomas Dibblee, provide services for free that benefit everyone. The former geologist for oil firms and the US Geological Survey says, ''I just like to be out in the mountains, seeing as much geology as I can see. I'm just doing what I like to do.''
Not all the winners were individuals. One was a labor union. Two were corporations - including a snack food firm in Dallas that came to the aid of a troubled airline.
Frito-Lay was cited for its work helping more than 5,000 employees of Braniff , who lost their jobs when the airline went bankrupt last year. The food firm set up a communications center where Braniff's unemployed could polish job-hunting skills and contact prospective employers. Seventy-five percent of those who used the service now have a job.
Other winners include the Hispanic Woman's Council, a Los Angeles group that develops leadership skills of low-income Hispanic women, and the Little Town Players, a Bedford, Va., theater group that performs drama for the area's schoolchildren.