How to run live project on localhost

You don't

Why would you want to do that?

Localhost is usually for development once developed you upload via FTP to a live hosting company whether it be a dedicated server or shared server the choice is yours there. There are ways to become your own host but I'm so sorry I don't have the answer on how to do that but it wouldn't be localhost you would still develop and then transfer the files to your real production server but unless you a large company only large companies usually do their own hosting for example I'm sure fedEx has their own servers ups probably has servers. Me, I use godaddy.

I have a client project that was running on live,now he need to modify and add some more features.That's why I want to run this project on my localhost.is it possible if yes then how?

So, you would need to pull the website down from the host. For example, connect to the server via FTP, download all of the assets, and run the server. Once finished making your modifications, you could either push to your repository if using git and pull on the server. Or if you're not using git, just re-upload the files you've changed to the server via FTP.

@b3zman41 great answer, and to add:

I do what your asking quite a bit (once a month or more). Get the files and if you need the data base up can dump a backup file too.

Add it to your local development environment, create a local db, run the backup (properly will need to open the backup and change some parameters). And you should have a mirror image. But, you should make sure you have a master saved locally(copy and paste) before digging in. Ftp (if you chose that route) on large sites and/or lots of content like videos can be a performance issue while your d/l to users that are using the site plus depending on the provider limitations.