web site deploy on internet

Question

I want to ensure a my web application (asp.net) works in all browser and its version normally when i will deploy it on internet (i use some function from JQuery it very necessary && design the site by CSS3 and Html5).
all things is working right with me when i develop the site (VS2012)
but i need a way to ensure all things will be alright when i deploy the site on internet.

any advice or website service or other ......................
thanks very much...