If the tables have the same structure:
INSERT INTO TARGET_TABLE SELECT * FROM SOURCE_TABLE;
If the tables have different structures:
INSERT INTO TARGET_TABLE (`col1`,`col2`) SELECT `col1`,`col2` FROM SOURCE_TABLE;
You can also add conditions:
INSERT INTO TARGET_TABLE (`col1_`,`col2_`) SELECT `col1`,`col2` FROM SOURCE_TABLE WHERE `foo`=1