On photoshop how do I make my backgrounds crisp white?

[turtle dove]

I often take studio images with a white background,sometimes (not always) the background can tend to have hints of grey or is just not white enough. How can I make my background crisp white without overexposing my subject?
step by step details on photoshop please :-D
thestril: great info thanks! dont you find using the lasso tool is timley and tricky and can sometimes cause unusual edging to the subject? (bodge jobby)