The 3 phases of reconstruction during the Civil War were Presidential Reconstruction (1863-66), Radical Reconstruction (1866-1873), and Redemption (1873-77).
Presidential Reconstruction, 1863-66 was controlled by Presidents Abraham Lincoln and Andrew Johnson, with the goal of quickly reuniting the country. It can be said to have begun with the Emancipation Proclamation. The programs proposed by Lincoln and subsequently by Johnson (who by late 1865 had lost the support of most of the Republican party) were opposed by the Radical Republicans.
The second phase of reconstruction occurred after the 1866 elections and began Congressional Reconstruction, 1866-1873 emphasizing civil rights and voting rights for the freedmen. Supported by the Military Reconstruction Act of 1867, in 1868 new state governments came to power in the former Confederacy which were based on a Republican coalition of freedmen, carpetbaggers and scalawags.
The third phase of reconstruction, the Redemption, 1873-1877, white Southern Democrats (calling themselves "Redeemers") defeated the Republicans and took control of each southern state, marking the end of Reconstruction. In 1877, President Rutherford Hayes withdrew federal troops, causing the collapse of the remaining three Republican state government.
For further reading, see Reconstruction: The Second Civil War.