Wow, Debbie - simple question, complicated answer! Bottom line, it's all very personal to you and your own body chemistry, the type of cancer you have, the type of chemo you had, what shape you're in physically... I'd offer that it probably takes longer than you'd think, certainly longer than you'd hope. Your hair will take months to grow back, and will probably grow back different than it was before - curly if it was straight, straight if it was curly, perhaps a different color and different thickness. You may have side effects that go on indefinitely - neuropathy (tingling) in the hands and feet is a typical side effect that lasts for a long time. (BTW, once you're done chemo, they're called "lasting effects," just so you have the lingo right.) Hot flashes induced by chemical menopause may last the rest of your life - or they may not. Or you may have your own personal lasting effects - that's one thing about cancer and chemo, we all approach it differently.
My advice would be to understand that chemo has done a number on you, and you'll heal, but it won't probably go as quickly as you'd like. Be patient; set your expectations to a reasonable level; and welcome each day, as it's one day farther out from chemo, one day closer to feeling normal - the "new normal."
As for how long the particular chemo cocktail you took will remain in your body - that's a question for your oncologist. Best of luck to you - PJH