While it's common to just rip your tie off by the time you get home - yanking it from your neck or simply making the loop just big enough to pull your head out - Unfortunately, this is the most damaging thing you could ever do. Instead, repeat all of the steps you followed to tie it but now do so in reverse order. While this method will not save on time, it'll definitely preserve it. Never leave knotted as it will permanently crease the fabric.
If you do not own a rack or organizer, simply wrap around your hand, beginning with the narrow end, and then put it onto a table or into a drawer and let it rest for a while. Iron (slightly warm) on the reverse side (if necessary).
Silk is a very delicate material and applying stain-removers can make matters worse. Test first on the back with spot remover or other mild-cleaning agents to be sure the remover won't damage it. Blot the stain, do not rub. You can also contact your local dry cleaner and ask for help. While dry cleaning will remove the stain in most cases, there's a chance that the shiny look and feel will also be gone.
Things to do:
Travel Tip: To prevent from being damaged in a tightly-packed suitcase, simply wrap and stick inside a shoe and go.