How do I tile my textures when I am in Texture-Paint Mode? When I draw in Texture-Paint Mode, the texture gets drawn on the surface but it is stretched out and it will not tile itself, or repeat itself, if you will.

I suppose one simple solution to this would be to make an image with the original image in it and just place copies next to each other, giving the illusion that it is indeed a repeated texture.
You can use a brush texture (1) for which you assign your brush image (2) and use it in texture paint mode and with the "tiled" option (3). So you have your object texture painted with it (4).



To have a more regular result, you can also assign the brush image to your object (in its material (5)) and stretch its UV map (6):