DNA should migrate towards the positive electrode. So if yours is not doing so there is clearly a problem. Check the pH of the electrophoresis buffers, makes sure the tanks have fresh buffer, make sure there is not an some sort of electrical short circuit, make sure you don't have a lot of salt in your DNA preparation, make sure it really is DNA that you are looking at and not some other macromolecule. And make sure there isn't something silly like your cables are reversed.
Electrophoresis gel boxes are an integral part of nucleic acid separation. A gel box is a container that can accommodate a gel tray and has electrodes that can be connected to a power supply. The electrodes on the gel box are usually color coded namely, black for the cathode and red for the anode.
The cathode carries the negative charge while the anode carries the positive charge. When the gel box is connected to a power supply, electrons enter through the cathode and leave through the anode. The flow of electrons sets up a potential energy difference between the electrodes and establishes an electric current. The gel box chamber holds the gel and is filled with a buffer prior to passing any electric current.
Before the DNA samples are added, the gel must be placed in a gel box. One end of the box is hooked to a positive electrode, while the other end is hooked to a negative electrode. The main body of the box, where the gel is placed, is filled with a salt-containing buffer solution that can conduct current.
Before the power to the gel box is turned on, and current begins to flow through the gel you need to see that the end of the gel with the wells is positioned towards the negative electrode. The end without wells (towards which the DNA fragments will migrate) is positioned towards the positive electrode. The DNA molecules have a negative charge because of the phosphate groups in their sugar-phosphate backbone, so they start moving through the matrix of the gel towards the positive pole.
So, the cathode (black leads) should be closer to the wells than the anode (red leads). Also, double check that the electrodes are plugged into the correct slots in the power supply.
Make sure that your agarose gel is oriented correctly in the electrophoresis chamber. If the gel is upside down, the DNA will run in the opposite direction.