The process will vary slightly depending on your EPiServer version, your Windows Server and SQL Server versions, and your IIS versions. But these are the basic steps involved:

1. WEB FILES
---

1.1 Get the complete Visual Studio project:

I'm assuming you want to be able to continue coding on the project in your dev environment, not just getting it to run on a local web server.

The live server probably only has the markup files (.aspx, .ascx etc), not the code and project files (.cs, .csproj etc), so you won't get the complete project from the live server. You (or your EPiServer partner) probably have the complete Visual Studio project in your source code repository, so do a checkout from there to a directory in your dev environment. 

2. DATABASE
----

2.1 Backup your live database(s):

You'll find the name of the database in your connectionstrings.config file in your live web site root. Copy those databases to your dev environment.

Two alternatives:
- either make a backup (yourdatabase.bak) file and copy to your dev environment
- or copy the yourdatabase.mdf and yourdatabase.ldf files to your dev environment.

2.2 Restore the database(s) on an SQL Server in your dev environment:

Two alternatives:
- either create a new database with the same name as the live db, then restore from the .bak file 
- or attach the database from the .mdf and .ldf files you copied from production
- then create a new SQL Server login with "owner" and "db_public" access to your restored database(s)

2.3 Setup database path in connectionstrings.config:

Modify the connectionstrings.config file in your dev environment to match the database and SQL login you created in step 2.2.

3. VPP FOLDERS
---

3.1 Copy the VPP folders:

You'll find the physical location of the VPP folders in your episerver.config file in your live web site root.
Copy those VPP folders to your dev environment.

3.2 Setup VPP paths in episerver.config:

Modify the episerver.config file in your dev environment to match the VPP folders you copied in step 3.1.

4. LICENSE
---

4.1 Get a dev license:

The EPiServer license from your live site is probably bound to the live server IP or MAC, so you can't use it in your dev environment.
Order a new EPiServer Development License from license.episerver.com (you might need your EPiServer partner to do this for you).
Put the license in your dev environment site root.