You may think about the steps below:
1, Backup your client's database and all site files and folders
2, Install local DB (database) environment and restore your client's database to local DB
3, Create a local folder and paste all site files and folders to local folder and setup appropriate permissions
4, Find hosts file under C:\Windows\System32\drivers\etc, and add one more entry, like 127.0.0.1 with your client's url
5, Create a new site (not application) through IIS Manager, point to the created folder and use the url in hosts file
6, You may need to modify connection string in web.config for your database if necessary
7, Use a browser to access you local site
If you have commercial version DNN, you can use Content Staging, which can hold your changes in development environment and then publish to production later.