To change half-full ink cartridges in an Epson NX110 printer, first ensure the printer is turned on and open the front cover to access the cartridges. Press the "Ink" button to move the cartridge holder to a reachable position. Carefully remove the old cartridges by pushing down on the tab and pulling them out, then insert the new cartridges until they click into place. Close the front cover, and the printer will automatically recognize the new cartridges.