I can give you an idea of how you can complete this but I'll not give you exact code so that you can do it by yourself. This is not very hard.
For modal you can use jQuery Colorbox plugin
] to create modal popup. There are many more plugins to create a popup. You can search on google for that. Now call the modal popup in jQuery document ready function, so that on page load the modal show up.
Now you can use asp button click event to save data on clicking the button. This will cause a postback and after postback you can call a function from backend to close the colorbox.
I hope this will help. Let me know if you stuck anywhere.