Most reintegrated into society like everyone else. There was a strong movement to prosecute them (mostly from Congress) but opposition from Lincoln, then Grant most notably put a stop to that.

Lee for instance lived in Richmond for a time then went to Lexington and became president of what became Washington and Lee University.

Longstreet bounced around in a few different companies after, and renewed a friendship with Grant, and eventually became the Ambassador to the Ottoman Empire!

When the was with Spain came in 1898 Joe Wheeler was appointed as the Commander of the US Cavalry forces sent to Cuba.

More personal to me the youngest General in the Army of Northern Virginia, General Lane, became the first Commandant of the Virginia Agricultural and Mechanical College which is known today as Virginia Tech. After a fist fight with another faculty member he then became one of the early leaders at Auburn University.

In general they attempted as best they could to move on with their lives, few ever rejoined the service, and most lived relatively undistinguished lives.

Of note though was the number of memoirs that they wrote, often slandering others and debating blame for various failures.