Shower daily using hot water to fade reddish tints from demi- or semi-permanent hair color. Shampoo your hair with a volumizing shampoo that opens up the hair follicles to help get the dye out quicker. This won't work for permanent dyes, but will strip red hues from temp colors without stressing your hair.
Cover up the red tints till they fade away. Apply a permanent or semi-permanent hair dye over your base color to camouflage the yucky red tones. If you choose a semi-permanent color, it needs to be darker than the dye you started with. Tones from the colors can clash. For example, going with a honey blond color over the red could leave you looking orangey in places. To neutralize red tones, look for dyes with green or drab undertones. Mix and apply the dye following manufacturer's instructions to shake up your look.
Pick up a color removal product to strip the reddish dye from your locks and get back to basics. Follow the directions on the color removal product to mix and apply the product, then rinse it off to find the red gone.
Head out in the sun to bleach the red to a coppery hue, if you like coppery tones but not the red you're stuck with. Put lemon juice on the red areas to help them pick up blonder notes, then stay out in the sun while the lemon juice dries. Repeat the lemon treatment till you're satisfied with the new color.
If you saw a stylist, check in with them within 72 hours of the dye job. You can fix hair color within this window, so the stylist can help you get back to a better color if you catch it in time.