I REALLY need to replace my entire shower, the doors, the base, the faucet. I am not sure how to measure the shower base. Can someone tell me how. And my next question is if I buy the base and doors and faucet from say Home Depot will they install it for me?

They will do an install at a price. Tell them you want them to measure it since they're doing the install. Avoid making an error that may cost you.