Mixing "hot" colors is often difficult. If you add white to most colors they'll merely become paler, while if you add black or other darker colors, your result will likely be a deeper but murkier color than what you had in mind. You can go to an art supply or hobby store and buy fluorescent paint; stores that carry this kind of material are likely to have hot pink or something like it in stock. However, if you're intent on mixing hot pink, or a close approximation, you can use colors you may already have in your paint kit.
Things You'll Need
Titanium or flake white
Lay out some alizarin crimson on your palette. You can find this color in oil paint, acrylic, tempera, gouache and watercolor. Regardless of your medium, the result will be approximately the same.
Add a small amount—about a match-head's size—of titanium or flake white to the alizarin crimson. With oil or acrylic, use a palette knife with a flexible blade to add white and mix the two colors. For gouache and watercolor, use your brush to move and mix colors. Rinse the brush before you dip it into a new color.
Mix in small increments of white until the paint begins to approximate the shade of hot pink you seek. If you're trying to match the color to something, coat the palette knife blade or brush hairs with the color you're mixing and hold it near the surface you're trying to match.
Add small amounts—half a match-head sized—of cadmium red if you find the mixture you have is too anemic. To make the color a bit deeper, add a wisp of pthalo blue, but make sure you use this color sparingly. It's extremely dark—darker than black—so it won't take much to change the character of the color you're mixing.