How does the human body make blood to replace whats lost when giving blood?

Bone marrow.

When you give blood your red cell volume and hence your oxygen carrying capacity decreases. This decrease in oxygen carrying capacity is called anemia, and no matter how mild, the cells of the kidneys detect this. They then secrete the hormone erythropoietin. This hormone travels to the bone marrow where there are hematopoietic stem cells (HSC). Typically, HSC makes all the cells of the blood (red cells, white cells and platelets) under the influence of certain hormones and cytokines. Erythropoietin influences HSC to proliferate and differentiate along the line that will become red cells and platelets. If you want more details, read on....

1) Erythropoietin (along with other factors) causes HSC to first differentiate into myeloid precursors. This is the family name for what will become the red cells, granulocytes and platelets. These precursors are called Colony Forming Unit Granulocyte, Erythrocyte, Monocyte Megakaryocyte (CFU GEMM).
2) Erythropoietin makes more of these precursor cells differentiate along the Erythrocyte line of GEMM. The Colony Forming Unit Erythrocyte (CFU E) results.
3) CFU E differentiate into Burst Forming Unit Erythrocyte (CBU E) Normoblast--> Polychromatophilic Erythroblast-->Orthochromatophilic Erythroblast-->Reticulocyte-->Mature Red Blood Cell

Your bone marrow is where your blood cells are made. When you loose blood, your body automatically makes more so that there's no harm to your body, or any harm done can be fixed.